Planar lightwave circuit, design method for wave propagation circuit, and computer program

ABSTRACT

A planar lightwave circuit is provided which can be easily fabricated by an existing planar-lightwave-circuit fabrication process, which can lower the propagation loss of signal light and which can convert inputted signal light so as to derive desired signal light. A planar lightwave circuit having a core and a clad which are formed on a substrate, has input optical waveguide(s) ( 111 ) which inputs signal light, mode coupling part ( 112 ) for coupling a fundamental mode of the inputted signal light to a higher-order mode and/or a radiation mode, or mode re-coupling part ( 113 ) for re-coupling the higher-order mode and/or the radiation mode to the fundamental mode, and output optical waveguide(s) ( 114 ) which outputs signal light. The mode coupling part or the mode re-coupling part is an optical waveguide which has core width and/or height varied continuously.

TECHNICAL FIELD

The present invention relates to a planar lightwave circuit forconverting inputted signal light and deriving desired signal light, adesign method for optimizing a wave propagation circuit, and a computerprogram for executing the design method.

BACKGROUND ART

With the still larger capacity and higher speed of an opticalcommunication system, it has become more important to provide an opticaldevice which carries out advanced functions at a low price. Since alightwave circuit fabricated on a planar substrate is highly versatilein design and is excellent in mass-producibility and stability, it canprovide the optical device meeting the requirement, and researches anddevelopments have therefore been made worldwidely.

Examples of prior-art planar lightwave circuits are shown in FIGS. 40through 42. The planar circuit shown in FIG. 40 is configured of aninput optical waveguide 171, and an output optical waveguide 172 whichis optically coupled to the input optical waveguide 171 (refer to, forexample, Patent Document 1). The planar lightwave circuit shown in FIG.40 has the output optical waveguide 172 designed in a parabolic shape,thereby to be endowed with the function of adjusting the fielddistribution of output signal light.

With the design technique, however, only the fundamental mode of inputsignal light and the second-order mode coupled thereto can be handled,so that a characteristic as a lens for adjusting the field distributionof the signal light has been inferior. Also, there has occurred theproblem that the size of the planar lightwave circuit becomes large onaccount of a configuration which gradually generates the second-ordermode.

Besides, there has been known a planar lightwave circuit which isendowed with a spot-size conversion function by a configuration whereinan optical waveguide of taper shape and its connection part with anoptical fiber are periodically divided (refer to, for example,Non-patent Document 1).

Since, however, the optical waveguide propagating a light signal isperiodically segmented, there is the problem that the reflection ofsignal light at each segmented surface is inevitable, and the planarlightwave circuit has had the drawback that it cannot be applied to anyother use than a spot size converter.

Besides, there has been known a planar lightwave circuit which isendowed with a spot-size conversion function by a configuration whereinthe width of an optical waveguide repeats increases and decreasesaperiodically (refer to, for example, Non-patent Document 2).

However, the optical waveguide width repeats abrupt increases anddecreases along the propagation direction of signal light, and hence,there has been the problem that the fabrication of the planar lightwavecircuit is very difficult.

Shown in FIG. 41 is the configuration of a lightwave circuit including aprior-art cross waveguide. The cross waveguide is indispensable as oneof basic constituents in the lightwave circuit. The lightwave circuit260 shown in FIG. 41 includes two input optical waveguides 261, twooutput optical waveguides 264, and an optical-waveguide crossing portion265 being a waveguide overlap portion which couples the two inputoptical waveguides 261 and the two output optical waveguides 264,respectively. The crossing angle 266 between the input optical waveguide261 and the output optical waveguide 264 needs to be narrowed forattaining reduction in the size of an optical device. However, as thecrossing angle 266 is made narrower, an optical coupling loss in theoptical-waveguide crossing portion 265 increases more, to pose theproblem that a crosstalk characteristic degrades more.

There has been known a cross waveguide which lowers an optical couplingloss in an optical-waveguide crossing portion in such a way that a spotsize in the optical-waveguide crossing portion is made larger than aspot size in the optical waveguide outside the optical-waveguidecrossing portion by making the width of the optical waveguide of theoptical-waveguide crossing portion smaller than the width of the opticalwaveguide outside the optical-waveguide crossing portion (refer to, forexample, Patent Document 2). Even in the structure of such a crosswaveguide, however, there has been the problem that the effect ofsufficiently lowering the optical coupling loss cannot be attained in acase where a crossing angle is smaller than 30°.

FIG. 42 shows the structural example of a prior-art optical branchcircuit. With the expansion of the application fields of opticalcommunication systems, the importance of planar lightwave circuits forbranching, multiplexing/demultiplexing and switching signal light(s) hasrisen more and more. Especially, the optical branch circuit forbranching or multiplexing the signal light(s) is indispensable as one ofbasic constituents in the lightwave circuit.

The optical branch circuit shown in FIG. 42 is configured of an inputoptical waveguide 371, an optical-waveguide branching portion 372,branched optical waveguides 373 a and 373 b, and output opticalwaveguides 374 a and 374 b (refer to, for example, Non-patent Document3). The signal light inputted to the input optical waveguide 371 isbranched by the optical-waveguide branching portion 372 as well as thebranched optical waveguides 373 a and 373 b, so as to be led to theoutput optical waveguides 374 a and 374 b. The optical branch circuit asshown in FIG. 42 is also called the “Y-branch circuit” because of itsshape.

As stated above, with the rapid spread of the optical communicationsystems, the importance of the lightwave circuit for branching anoptical signal, switching optical paths, or multiplexing/demultiplexingoptical signals/an optical signal every wavelength has increased. Forbuilding and providing an optical communication system of highperformance, it is indispensable to design and realize a lightwavecircuit of high performance.

The lightwave circuit can be designed by combining individual lightwavecircuit elements such as a channel optical waveguide, a taper opticalwaveguide and an optical slab waveguide. However, when such a designmethod is employed, it is impossible to create a function which cannotbe realized by the combination of the prior-art lightwave circuitelements, for example, a spot size converter of very small length. Insuch a case, the design of the lightwave circuit has heretofore beencarried out by employing an optimization technique of cut-and-try type,such as genetic algorithm.

FIG. 43 is a chart representing a design method for a lightwave circuitas is based on a prior-art genetic algorithm (refer to, for example,Non-patent Document 4).

The prior-art algorithm in FIG. 43 includes the step 301 of giving theinitial values of refractive index distributions, the step 302 ofvarying the refractive index distributions in accordance with thegenetic algorithm, the step 303 of evaluating the varied refractiveindex distributions by actually propagating light, the step 304 ofselecting favorable refractive index distributions, and the step 305 ofjudging if the obtained refractive index distributions satisfy desiredcharacteristics. The algorithm first proceeds along the steps 301, 302,303, 304 and 305, and when the desired characteristics are not obtainedat the step 305, the steps 302 through 304 are iterated until thedesired characteristics are obtained.

Here, at the step 302 of the prior-art algorithm, the refractive indexdistribution is altered in accordance with the genetic algorithm.Whether or not the alteration is a change in a better direction has notbeen known before the light is actually propagated at the step 305.

FIGS. 44A and B show a lightwave circuit (this example is a spot sizeconverter) designed in accordance with the prior-art genetic algorithm(in, for example, Non-patent Document 2).

The lightwave circuit shown in FIGS. 44A and B has a structure in whicha core 401 having a constant thickness is embedded in a clad layer 402.

When a light propagation direction is assumed to be along a z-axis, FIG.44A is a drawing in which a refractive index distribution on a y-axis isobserved from the direction of an x-axis, and FIG. 44B is a drawing inwhich a refractive index distribution on the x-axis is observed from thedirection of the y-axis. In the prior-art lightwave circuit shown inFIGS. 44A and B, the optimization of the lightwave circuit is realizedin such a way that, as shown in FIG. 44B, the refractive indexdistribution is divided into segments of constant lengths (3 μm in thisexample) in the z-axial direction, whereupon the x-axial widths of therespective segments are adjusted in accordance with the geneticalgorithm.

Patent Document 1: Japanese Patent Application Laid-open No. 9-297228(FIG. 7)

Patent Document 2: Japanese Patent Application Laid-open No. 5-60929

Non-patent Document 1: Z. Waissman with one other, “Analysis ofPeriodically Segmented Waveguide Mode Expanders”, Journal of LightwaveTechnology, October 1995, Vol. 13, No. 10 (FIG. 1)

Non-patent Document 2: Michael M. Spuhler with four others, “A VeryShort Planar Silica Spot-Size Converter Using a Nonperiodic SegmentedWaveguide”, Journal of Lightwave Technology, September 1998, Vol. 16,No. 9 (FIG. 1 and FIG. 2)

Non-patent Document 3: Katsunari Okamoto, “Fundamentals of OpticalWaveguides”, 2000 Academic Press (FIGS. 7 and 15)

Non-patent Document 4: B. Plaum with three others, “Optimization ofwaveguide bends and bent mode converters using a genetic algorithm”,25th International Conference on Infrared and Millimeter Waves(IRMMW2000), Sep. 12-15, 2000

DISCLOSURE OF THE INVENTION

Regarding the prior-art planar lightwave circuit which is designed withthe propagation mode of the optical waveguide set at the fundamentalmode as described in connection with FIG. 40, there has been the problemthat a light field which can be realized is limited, and regarding theprior-art planar lightwave circuit whose function is realized by thesegmentation of the optical waveguide, there has been the problem thatthe reflected light, etc. appear due to the abrupt variation of thewaveguide width, so the lightwave circuit cannot be utilized as atransmission type device. These planar lightwave circuits have had theproblem that very fine optical waveguides need to be realized, so thefabrications are very difficult.

Besides, the lightwave circuit which includes the prior-art crosswaveguide as described in connection with FIG. 41 has had the problemthat the optical coupling loss in the optical-waveguide crossing portionis heavy.

In the prior-art optical branch circuit described in connection withFIG. 42, a branching angle 375 needs to be widened for shortening theY-branch circuit and reducing the size thereof. In a case where thebranching angle 375 is wide, the branch circuit becomes a structure inwhich the core width of the optical waveguide is abruptly expanded inthe optical-waveguide branching portion 372. On this occasion, thehigher-order mode of the signal light is excited in theoptical-waveguide branching portion 372, resulting in the problem thatthe optical coupling loss of the signal light enlarges.

Also, there has been the drawback that the branching ratio of the signallight deviates from a desired design value and becomes unstable due tothe appearance of the higher-order mode mentioned above. For thesereasons, there has been a limit to further reduction in the size of theoptical branch circuit. Besides, the prior-art optical branch circuithas had the drawback that, also in a case where the first-order modemixes in the signal light, in addition to the fundamental mode, theactual branching ratio deviates from the desired design value, so theprecision of the branching ratio degrades much.

In this manner, the prior-art optical branch circuit has had theproblems that the optical coupling loss in the branching portion isheavy, and that the branching ratio is unstable.

According to one aspect of the present invention, there is provided anoptical branch circuit of low loss and stable branching ratio as can befabricated using the prior-art lightwave-circuit fabrication technique.Besides, according to one aspect of the invention, there is provided anoptical branch circuit in which a branching angle is made wider than inthe prior-art optical branch circuit and which has its size furtherreduced as a whole.

With the prior-art lightwave-circuit design method described inconnection with FIGS. 44A and B, the cut-and-try type algorithm isemployed, and it has therefore been necessary to input an input field tothe lightwave circuit and evaluate an output field after the propagationeach time the lightwave circuit is varied. In this manner, the prior-artlightwave-circuit design method has had the problem that thecomputations of wave propagations must be executed as to whether therefractive index of a certain part is to be increased or decreased, so acomputing time period becomes very long.

Further, for the reason of the long computing time period, it has beenvery difficult to freely alter and study the lightwave circuit, with theprior-art lightwave-circuit design method.

In, for example, the prior-art lightwave circuit shown in FIGS. 44A andB, the refractive index distribution has been divided into the segments,and only the width in the x-axial direction has been varied (refer to,for example, Non-patent Document 2). The reason therefor has been that,unless such limitations are placed, the computing time period becomestoo enormous to actually obtain a solution.

One aspect of the present invention consists in a planar lightwavecircuit having a core and a clad which are formed on a substrate,characterized by comprising at least one input optical waveguide whichinputs signal light; mode coupling means for coupling a fundamental modewhich is part of the inputted signal light, to at least either of ahigher-order mode and a radiation mode, or mode re-coupling means forre-coupling at least either of the higher-order mode and the radiationmode to the fundamental mode; and at least one output optical waveguidewhich outputs signal light; the mode coupling means or the modere-coupling means being an optical waveguide which has at least one of acore width and height varied continuously.

According to the invention, there is provided a planar lightwave circuitwhich can be easily fabricated by an existing planar-lightwave-circuitfabrication process, in which the propagation loss of signal light islowered, and which can convert the inputted signal light so as to derivedesired signal light.

One aspect of the invention consists in a planar lightwave circuitincluding an optical waveguide lens which has a core and a clad formedon a substrate, characterized in that the optical waveguide lenscomprises at least one input optical waveguide which inputs signallight; mode coupling means for coupling part of the inputted signallight to a higher-order mode and a radiation mode; mode re-couplingmeans for re-coupling the signal light coupled to the higher-order modeand the radiation mode by the mode coupling means, to output signallight; and at least one output optical waveguide for outputting theoutput signal light; the mode coupling means and the mode re-couplingmeans being optical waveguides each of which has at least one of a corewidth and height varied continuously.

According to the invention, there is provided a planar lightwave circuitincluding an optical waveguide lens, which can be easily fabricated byan existing planar-lightwave-circuit fabrication process and in whichthe propagation loss of signal light is lowered.

One aspect of the invention consists in a planar lightwave circuitincluding a cross waveguide in which at least two optical waveguideshaving a core and a clad formed on a substrate cross, characterized inthat the cross waveguide comprises at least two input optical waveguideswhich input signal light; mode coupling means for coupling part of theinputted signal light to a higher-order mode and a radiation mode; modere-coupling means for re-coupling the signal light coupled to thehigher-order mode and the radiation mode by the mode coupling means, tooutput signal light; at least two output optical waveguides which outputthe output signal light, and an optical-waveguide crossing portion beinga part at which two virtual optical waveguides rectilinearly extendingfrom the input waveguides toward the output waveguides overlap; the modecoupling means and the mode re-coupling means being optical waveguideseach of which has a core width varied continuously; theoptical-waveguide crossing portion being such that a core width of anoptical waveguide at a position between an end of the optical-waveguidecrossing portion on a side of the input optical waveguides and a centralpart of the optical-waveguide crossing portion is greater than the corewidth of the optical waveguide at an end of the optical-waveguidecrossing portion on the side of the input optical waveguides and thecore width of the optical waveguide at the central part of theoptical-waveguide crossing portion, and that the core width of theoptical waveguide at a position between the central part of theoptical-waveguide crossing portion and an end of the optical-waveguidecrossing portion on a side of the output optical waveguides is greaterthan the core width of the optical waveguide at the central part of theoptical-waveguide crossing portion and the core width of the opticalwaveguide at the end of the optical-waveguide crossing portion on theside of the output optical waveguides.

According to the invention, there is provided a planar lightwave circuitincluding a cross waveguide, which is of low loss and high crosstalkcharacteristic.

One aspect of the invention consists in a planar lightwave circuitincluding an optical branch circuit which has a core and a clad formedon a substrate, characterized in that the optical branch circuitcomprises one input optical waveguide which inputs signal light; modecoupling means for coupling part of the inputted signal light to ahigher-order mode and a radiation mode; mode re-coupling means forre-coupling the signal light coupled to the higher-order mode and theradiation mode by the mode coupling means, to output signal light; andat least two output optical waveguides which output the output signallight; the mode coupling means and the mode re-coupling means beingoptical waveguides each of which has a core width varied continuously.

According to the invention, there is provided a planar lightwave circuitincluding an optical branch circuit, which can be fabricated using aprior-art lightwave-circuit fabrication technique, and which is of lowloss and stable branching ratio. Besides, according to one aspect of theinvention, there is provided a planar lightwave circuit including anoptical branch circuit, in which a branching angle is made larger thanin a prior-art optical branch circuit, and which is made still smallerin size as a whole.

One aspect of the invention consists in a planar lightwave circuitincluding a slab type coupler which has a core and a clad formed on asubstrate, characterized in that the slab type coupler comprises atleast one, first input/output optical waveguide which inputs/outputs alight signal; an optical slab waveguide which is optically connected tothe first input optical waveguide; and at least two, second input/outputoptical waveguides which are optically connected to the optical slabwaveguide, and which input/output light signals; and that the secondinput/output optical waveguides comprise mode coupling means forcoupling part of the inputted/outputted signal light to at least eitherof a higher-order mode and a radiation mode, and converting the coupledpart into a plane wave at an end of the optical slab waveguide; the modecoupling means being an optical waveguide which has a core width variedcontinuously.

According to the invention, there is provided a planar lightwave circuitincluding a slab type coupler, which can be easily fabricated by anexisting planar-lightwave-circuit fabrication process, and which is oflow loss.

One aspect of the invention consists in a planar lightwave circuitincluding an arrayed waveguide grating filter which has a core and aclad formed on a substrate, characterized in that the arrayed waveguidegrating filter comprises at least one input optical waveguide whichinputs signal light; a first optical slab waveguide which is opticallyconnected with the input optical waveguide; arrayed optical waveguideswhich are optically connected with the first optical slab waveguide, andwhich become longer with a predetermined waveguide length difference insuccession; a second optical slab waveguide which is optically connectedto the arrayed optical waveguides; and at least one output opticalwaveguide which is optically connected to the second optical slabwaveguide; and that each of the arrayed optical waveguides comprisesmode re-coupling means for re-coupling a higher-order mode and aradiation mode to the signal light, at a part optically touching thefirst optical slab waveguide; and mode coupling means for coupling thesignal light to the higher-order mode and the radiation mode, at a partoptically touching the second optical slab waveguide; the mode couplingmeans and the mode re-coupling means being optical waveguides each ofwhich has a core width varied continuously.

According to the invention, there is provided a planar lightwave circuitincluding an arrayed waveguide grating filter, which can be easilyfabricated by an existing planar-lightwave-circuit fabrication process,and which is of low loss.

One aspect of the invention consists in a method wherein a wavepropagation circuit for obtaining a desired output field from an inputfield is designed by employing a computer, characterized by comprising arefractive-index-distribution initialization step of storing initialvalues of a refractive index distribution of a propagation medium in thewave propagation circuit, in storage means of the computer; a step ofsetting any position of the transmission medium in a wave propagationdirection thereof, as an optimized position; an optimized-positioninput/output-field computation step of computing a field in a case wherethe input field has propagated forwards from an inlet of the wavepropagation circuit to the optimized position, and a field in a casewhere the desired output field has propagated backwards from an outputof the wave propagation circuit to the optimized position, and thenstoring the fields in the storage means of the computer; and arefractive-index-distribution alteration step of adjusting therefractive index distribution at the optimized position so thatwavefronts of the field in the case where the input field has propagatedforwards and the field in the case where the desired output field haspropagated backwards may agree; the optimized-position setting step, theoptimized-position input/output-field computation step and therefractive-index-distribution alteration step being iterated while theoptimized position is being changed in the wave propagation circuit.

One aspect of the invention consists in a method wherein a wavepropagation circuit for obtaining a desired output field from an inputfield is designed by employing a computer, characterized by comprising arefractive-index-distribution initialization step of storing initialvalues of a refractive index distribution of a propagation medium in thewave propagation circuit, in storage means of the computer; a step ofsetting an outlet of the wave propagation circuit as an optimizedposition; a forward-propagation input-field-distribution computationstep of computing a field distribution in a case where the input fieldhas propagated forwards from an inlet of the wave propagation circuit tothe output thereof, and storing the field distribution in the storagemeans of the computer; a backward-propagation optimized-positionoutput-field computation step of computing a field in a case where theoutput field has propagated backwards from the outlet of the wavepropagation circuit to the optimized position, and storing the field inthe storage means of the computer; and a refractive-index-distributionalteration step of adjusting the refractive index distribution at theoptimized position so that wavefronts of the field in the case where theinput field has propagated forwards and the field in the case where thedesired output field has propagated backwards may agree; thebackward-propagation optimized-position output-field computation stepand the refractive-index-distribution alteration step being iteratedwhile the optimized position is being successively changed from theoutlet to the inlet along a wave propagation direction.

One aspect of the invention consists in a method wherein a wavepropagation circuit for obtaining a desired output field from an inputfield is designed by employing a computer, characterized by comprising arefractive-index-distribution initialization step of storing initialvalues of a refractive index distribution of a propagation medium in thewave propagation circuit, in storage means of the computer; a step ofsetting an inlet of the wave propagation circuit as an optimizedposition; a backward-propagation output-field-distribution computationstep of computing a field distribution in a case where the output fieldhas propagated backwards from an outlet of the wave propagation circuitto the input thereof, and storing the field distribution in the storagemeans of the computer; a forward-propagation optimized-positioninput-field computation step of computing a field in a case where theinput field has propagated forwards from the inlet of the wavepropagation circuit to the optimized position, and storing the field inthe storage means of the computer; and a refractive-index-distributionalteration step of adjusting the refractive index distribution at theoptimized position so that wavefronts of the field in the case where theinput field has propagated forwards and the field in the case where thedesired output field has propagated backwards may agree; theforward-propagation optimized-position input-field computation step andthe refractive-index-distribution alteration step being iterated whilethe optimized position is being successively changed from the inlet tothe outlet along a wave propagation direction.

According to the invention, there are provided a method which designs anoptimized wave propagation circuit at high speed, and a computer programwhich executes the method.

Besides, a design method for a wave propagation circuit as is not of acut-and-try type, but as is deterministic is provided by employing adesign method for a wave propagation circuit in one aspect of theinvention.

Further, according to one aspect of the invention, there is provided amethod which optimizes a wave propagation circuit at high speed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a configurational view of an optical waveguide lens (planarlightwave circuit) in a first embodiment.

FIG. 2 is a diagram showing the wavelength-dependency properties of thepropagation loss of the signal light of the optical waveguide lens(planar lightwave circuit) in the first embodiment.

FIG. 3 is a configurational view of an optical waveguide lens (planarlightwave circuit) in a second embodiment.

FIG. 4 is a plan view of a planar lightwave circuit in a thirdembodiment.

FIG. 5 is a sectional view of the planar lightwave circuit in the thirdembodiment.

FIG. 6A is a view showing the fabrication process of the planarlightwave circuit in the third embodiment.

FIG. 6B is a view showing the fabrication process of the lightwavecircuit in the third embodiment.

FIG. 6C is a view showing the fabrication process of the lightwavecircuit in the third embodiment.

FIG. 6D is a view showing the fabrication process of the lightwavecircuit in the third embodiment.

FIG. 7 is a view representing the configuration of a planar lightwavecircuit in a fourth embodiment.

FIG. 8 is a view representing the configuration of another planarlightwave circuit in the fourth embodiment.

FIG. 9 is a diagram showing the wavelength-dependencies of thepropagation losses of cross waveguides in the fourth embodiment and aprior-art example.

FIG. 10 is a diagram showing the wavelength-dependencies of thecrosstalk characteristics of the cross waveguides in the fourthembodiment and the prior-art example.

FIG. 11 is a flow chart showing a computation procedure for determiningthe refractive index distribution of the planar lightwave circuit in thefourth embodiment.

FIG. 12 is a configurational view of a crossing planar lightwave circuitin a fifth embodiment.

FIG. 13 is a diagram showing the wavelength-dependency properties of thepropagation loss of the signal light of the crossing planar lightwavecircuit in the fifth embodiment.

FIG. 14 is a view representing the configuration of a crossing planarlightwave circuit in a sixth embodiment.

FIG. 15 is a view representing the configuration of an optical branchcircuit in a seventh embodiment.

FIG. 16 is a view representing the configuration of another opticalbranch circuit in the seventh embodiment.

FIG. 17 is a diagram showing the wavelength-dependencies of thepropagation losses of the optical branch circuit in the seventhembodiment and an optical branch circuit in a prior-art example.

FIG. 18 is a flow chart showing a computation procedure for determiningthe refractive index distribution of the optical branch circuit in theseventh embodiment.

FIG. 19 is a view representing the configuration of an optical branchcircuit in an eighth embodiment.

FIG. 20 is a diagram showing the wavelength-dependencies of thepropagation losses of the optical branch circuit in the eighthembodiment.

FIG. 21 is a configurational view of a slab type coupler in a ninthembodiment.

FIG. 22 is a diagram representing the characteristic of the slab typecoupler in the ninth embodiment.

FIG. 23A is a configurational view of an arrayed waveguide gratingfilter in a tenth embodiment.

FIG. 23B is an enlarged view of the arrayed waveguide grating filter inthe tenth embodiment.

FIG. 23C is an enlarged view of the arrayed waveguide grating filter inthe tenth embodiment.

FIG. 24 is a diagram representing the characteristic of the arrayedwaveguide grating filter in the tenth embodiment.

FIG. 25 is a chart showing the algorithm of a method of designing a wavepropagation circuit in an eleventh embodiment.

FIG. 26 is a diagram representing the initial values of a refractiveindex distribution in the method of designing the wave propagationcircuit in the eleventh embodiment.

FIG. 27A is a diagram representing how to give the refractive indexdistribution in the method of designing the wave propagation circuit inthe eleventh embodiment.

FIG. 27B is a diagram representing how to give the refractive indexdistribution in the method of designing the wave propagation circuit inthe eleventh embodiment.

FIG. 28 is a diagram representing the alteration magnitude of therefractive index distribution in the method of designing the wavepropagation circuit in the eleventh embodiment.

FIG. 29 is a diagram representing the characteristic of a lightwavecircuit which has been designed by the method of designing the wavepropagation circuit in the eleventh embodiment.

FIG. 30 is a chart showing the algorithm of a method of designing a wavepropagation circuit in a twelfth embodiment.

FIG. 31 is a diagram representing the initial values of a refractiveindex distribution in the method of designing the wave propagationcircuit in the twelfth embodiment.

FIG. 32A is a diagram representing how to give the refractive indexdistribution in the method of designing the wave propagation circuit inthe twelfth embodiment.

FIG. 32B is a diagram representing how to give the refractive indexdistribution in the method of designing the wave propagation circuit inthe twelfth embodiment.

FIG. 33 is a diagram representing the refractive index distribution of alightwave circuit which has been designed by the method of designing thewave propagation circuit in the twelfth embodiment.

FIG. 34A is a diagram representing the characteristic of the lightwavecircuit which has been designed by the method of designing the wavepropagation circuit in the twelfth embodiment.

FIG. 34B is a diagram representing the characteristic of the lightwavecircuit which has been designed by the method of designing the wavepropagation circuit in the twelfth embodiment.

FIG. 35 is a chart showing the algorithm of a method of designing a wavepropagation circuit in a thirteenth embodiment.

FIG. 36 is a diagram representing the initial values of a refractiveindex distribution in the method of designing the wave propagationcircuit in the thirteenth embodiment.

FIG. 37A is a diagram representing how to give the refractive indexdistribution in the method of designing the wave propagation circuit inthe thirteenth embodiment.

FIG. 37B is a diagram representing how to give the refractive indexdistribution in the method of designing the wave propagation circuit inthe thirteenth embodiment.

FIG. 38 is a diagram representing the refractive index distribution of alightwave circuit which has been designed by the method of designing thewave propagation circuit in the thirteenth embodiment.

FIG. 39 is a diagram representing the characteristic of the lightwavecircuit which has been designed by the method of designing the wavepropagation circuit in the thirteenth embodiment.

FIG. 40 is a view representing the configuration of a prior-art planarlightwave circuit.

FIG. 41 is a view representing the configuration of a prior-art crosswaveguide.

FIG. 42 is a view representing the configuration of a prior-art Y-branchwaveguide.

FIG. 43 is a chart showing the algorithm of a prior-art method ofdesigning a wave propagation circuit.

FIG. 44A shows an example of a lightwave circuit which has been designedby the prior-art method of designing the wave propagation circuit.

FIG. 44B shows an example of a lightwave circuit which has been designedby the prior-art method of designing the wave propagation circuit.

BEST MODE FOR CARRYING OUT THE INVENTION

Now, embodiments of the present invention will be described in detail inconjunction with the drawings. By the way, in the embodiments, partshaving the same functions will be assigned the same reference numeralsand signs, and they shall not be repeatedly described.

Further, in each of the ensuing embodiments, a planar lightwave circuitwill be assumed an optical waveguide of silica-based glass formed on asilicon substrate. This is because such a combination can provide aplanar lightwave circuit which is stable and which is of excellentworkability. However, the invention is not restricted to thecombination, but it may, of course, employ other substrates and glassfilms such as a semiconductor optical waveguide and a polymer opticalwaveguide.

First Embodiment

The first embodiment of the invention will be described with referenceto FIGS. 1 and 2.

FIG. 1 is a plan view in which an optical waveguide lens (planarlightwave circuit) according to the first embodiment is seen in adirection perpendicular to a substrate. A z-axis indicates thepropagation direction of signal light. Here, the optical waveguide lensis supposed in FIG. 1, and this is because the planar lightwave circuitaccording to the invention is excellent for realizing the lens or thelike function which is difficult to be realized by only a propagationmode. However, the planar lightwave circuit according to the inventionis not restricted to this embodiment, but it can be configured as aplanar lightwave circuit having another function, such as spot sizeconverter.

As shown in FIG. 1, the optical waveguide lens (planar lightwavecircuit) according to the first embodiment is configured of an inputoptical waveguide 111 which inputs the signal light, mode coupling means112 for coupling part of the signal light inputted to the input opticalwaveguide 111, to a higher-order mode and a radiation mode, modere-coupling means 113 for re-coupling the higher-order mode and theradiation mode optically coupled in the mode coupling means 112, tooutput signal light in consideration of phases, and an output opticalwaveguide 114 which outputs the output signal light optically re-coupledin the mode re-coupling means 113.

The mode coupling means 112 and the mode re-coupling means 113 areconfigured of an optical waveguide whose core width is variedaperiodically smoothly or continuously.

There will be described a method of forming the modulated core width ofthe optical waveguide of the optical waveguide lens shown in FIG. 1. Themodulated core width of the optical waveguide is determined by applyingthe fundamental concept of a wave transmission medium. Here, the “wave”which is propagated through the wave transmission medium is “light”because of the application to the lightwave circuit. A theory concerningthe wave transmission medium designates the characteristic of the mediumon the basis of a general wave equation, and it can, in principle, holdtrue of a general wave.

Ψ is let denote a field (forward propagating light) which is obtained insuch a way that the field of the signal light inputted from the inputoptical waveguide 111 is propagated from the side of the input opticalwaveguide 111 onto the side of the output optical waveguide 114, whileΦ* is let denote a field (backward propagating light) which is obtainedin such a way that a field obtained by inverting the phase of the fieldof the desired signal light to be outputted from the output opticalwaveguide 114 is propagated from the side of the output opticalwaveguide 114 onto the side of the input optical waveguide 111.

On this occasion, when a refractive index distribution is given so as tominimize the phase differences between the forward propagating light Ψand the backward propagating light Φ* at the individual positions of thez-axis shown in FIG. 1, the optimal optical waveguide lens (planarlightwave circuit) for converting the inputted signal light into thedesired output signal light can be configured.

Concretely, the phase differences (Ψ−Φ*) between the forward propagatinglight and the backward propagating light at the interface of a core anda clad are computed at the individual positions of the z-axis shown inFIG. 1.

In a case where the phase difference between the forward propagatinglight and the backward propagating light at the interface of the coreand the clad is positive (Ψ−Φ*>0), this phase difference between Ψ andΦ* can be minimized by enlarging the core width of the opticalwaveguide.

Besides, in a case where the phase difference between the forwardpropagating light and the backward propagating light at the interface ofthe core and the clad is negative (Ψ−Φ*<0), this phase differencebetween Ψ and Φ* can be minimized by reducing the core width of theoptical waveguide.

The core widths of the optical waveguide as minimize the phasedifferences between the forward propagating light Ψ and the backwardpropagating light Φ* at the individual positions of the z-axis arerespectively evaluated by computations on the basis of such a formationmethod, whereby the optimal optical waveguide lens (planar lightwavecircuit) for converting the inputted signal light into the desiredoutput signal light can be configured.

Here, in a case where the variation of the core width of the opticalwaveguide is abrupt relative to the propagation direction of the signallight, there occurs the problem that the fabrication of the planarlightwave circuit becomes difficult. Accordingly, the variation of thecore width of the optical waveguide should desirably be continuous andsmooth and be ±8.0 μm per unit length (1 μm) in the signal-lightpropagation direction. Further, the optimal value of the variation ofthe core width of the optical waveguide should more desirably lie withina range of −4.0 μm through +4.0 μm per unit length (1 μm) in thesignal-light propagation direction.

The optical waveguide lens (planar lightwave circuit) shown in FIG. 1can be fabricated by a procedure as stated below. An under claddinglayer of SiO₂ is first deposited on an Si substrate by flame hydrolysisdeposition or the like, and a core layer of SiO₂ glass which is dopedwith GeO₂ as a dopant is subsequently deposited. Next, the core layer isetched by employing a pattern as shown in FIG. 1, so as to smoothen thevariation of the core width of the optical waveguide, thereby tofabricate an optical waveguide portion. Lastly, an over cladding layerof SiO₂ is deposited again.

Shown in FIG. 2 is the wavelength-dependency properties of thepropagation loss of the signal light in the case where the planarlightwave circuit of the invention has been configured as the opticalwaveguide lens. This dependency is based on the optical waveguide lensin the case where the variation of the core width of the opticalwaveguide has been limited within the range of −4.0 through +4.0 μm perμm. It is understood from FIG. 2 that the propagation loss of the signallight is lowered to about 0.1 dB in a wavelength band of 1300-1600 nm,so a sufficiently favorable characteristic is attained.

Second Embodiment

Next, the second embodiment of the present invention will be describedwith reference to FIG. 3.

An optical waveguide lens (planar lightwave circuit) according to thesecond embodiment is a modification to the optical waveguide lens(planar lightwave circuit) according to the first embodiment.

FIG. 3 is a plan view in which the optical waveguide lens (planarlightwave circuit) according to the second embodiment is seen in adirection perpendicular to a substrate. A z-axis indicates thepropagation direction of signal light. Mode coupling means 112 and modere-coupling means 113 are configured unitarily as modecoupling/re-coupling means 131. Incidentally, the modulated core widthof a waveguide can be formed by the same method as that of the opticalwaveguide lens (planar lightwave circuit) of the first embodiment.

As shown in FIG. 3, the mode coupling means 112 and the mode re-couplingmeans 113 need not have the configurations independent of each other asshown in FIG. 1, but it is possible to adopt a configuration in which aninput optical waveguide 111, the mode coupling/re-coupling means 131with the mode coupling means 112 and the mode re-coupling means 113united, and an output optical waveguide 114 are optically coupled inthis order.

Third Embodiment

Next, the third embodiment will be described with reference to FIGS. 4through 6.

Whereas the above embodiments have indicated the examples of the planarlightwave circuits in each of which the core width of the opticalwaveguide is varied in the direction parallel to the substrate, a planarlightwave circuit in the third embodiment according to the inventionindicates an example in which the core width of a waveguide is varied ina direction perpendicular to a substrate, that is, in a depthwisedirection.

Even when the core width of the waveguide is varied in the directionperpendicular to the substrate, similar advantages can be attained.Signal light has the property that a distribution is more liable tospread in the depthwise direction. Therefore, when the core width isvaried in the depthwise direction, a rather greater advantage isattained, that is, the advantage of lowering a loss attendant uponpropagation is enhanced.

Shown in FIGS. 4 and 5 is the example of the waveguide (planar lightwavecircuit) in which the core width of the optical waveguide is varied inthe depthwise direction. FIG. 4 is a plan view in which the waveguide isseen in the direction perpendicular to the substrate. FIG. 5 is asectional view taken along VIII in FIG. 4.

A fabrication method is shown in FIGS. 6A through 6D. A polymer clad 116is formed on a substrate 110 by an ordinary method, and it is coatedwith a photosensitive resin 115 which is to form a core. The uppersurface of the resulting structure is irradiated with and scanned byultraviolet radiation or the like. On that occasion, only parts to formthe core are irradiated, resinified and hardened (FIG. 6A). Thereafter,when unhardened parts are rinsed away, only the parts to form the coreremain (FIG. 6B).

Subsequently, the resulting structure is coated with a photosensitiveresin 106 of low refractive index as is to form a clad, so as to havethe same film thickness as that of the coating of the photosensitiveresin forming the core as was applied in FIG. 6A, and to have the samefilm thickness as that of the remaining parts to form the core, and thephotosensitive resin 106 is irradiated and hardened over its whole area,thereby to obtain a uniform flat surface 102 (not illustrated).

Further, the uniform flat surface 102 is coated with a photosensitiveresin 115 which is to form a core, and the upper surface of which isirradiated with and scanned by ultraviolet radiation or the like,whereby only parts to form the core are resinified and hardened (FIG.6C). Thereafter, unhardened parts are rinsed away, and a resin to form aclad is applied and hardened. Such processes are repeated, whereby thewaveguide whose core width is varied in the depthwise direction as shownin FIG. 5 can be obtained (FIG. 6D).

When the propagation loss of the planar lightwave circuit employing thewaveguide is measured, 0.03 dB is exhibited as in the planar circuitemploying the waveguide whose core width is varied in the planardirection.

Fourth Embodiment

The fourth embodiment of the present invention will be described withreference to FIGS. 7 through 11.

FIG. 7 is a plan view in which a cross waveguide (planar lightwavecircuit) in the fourth embodiment according to the invention is seen ina direction perpendicular to a substrate. As shown in FIG. 7, the planarlightwave circuit 210 of this embodiment includes two input opticalwaveguides 211 to which signal light is inputted, mode coupling means212 for coupling part of the signal light inputted to the input opticalwaveguide 211, to a higher-order mode or a radiation mode, modere-coupling means 213 for re-coupling the signal light coupled to theoptical high-order mode or radiation mode in the mode coupling means212, to output signal light in consideration of phases, two outputoptical waveguides 214 which output the output signal light opticallyre-coupled in the mode re-coupling means 213, and an optical-waveguidecrossing portion 215 in which two virtual optical waveguides 211′rectilinearly extending from the input waveguides 211 toward the outputwaveguides 214 or two virtual optical waveguides 214′ rectilinearlyextending from the output waveguides 214 toward the input waveguides 211overlap.

In the planar lightwave circuit 210 shown in FIG. 7, the mode couplingmeans 212, mode re-coupling means 213 and the optical-waveguide crossingportion 215 are not limited to the illustrated positions, but they canalso be configured so as not to overlap one another. Further, opticalwaveguides whose core widths are not varied can be interposed.

In FIGS. 7 and 8, a z-axis indicates the propagation direction of thesignal light. Besides, w1, w2, w3, w4 and w5 indicate the core widths ofthe optical waveguides at z-axial coordinates z1, z2, z3, z4 and z5(z1<z2<z3<z4<z5) shown in the figures, respectively. The coordinate z1corresponds to the ends of the input waveguides 211 in theoptical-waveguide crossing portion 215. The coordinate z5 corresponds tothe ends of the output waveguides 214 in the optical-waveguide crossingportion 215. The coordinate z3 corresponds substantially to the centerof the optical-waveguide crossing portion 215. Besides, a crossing angle216 in this embodiment signifies the crossing angle between the virtualoptical waveguides 211′ and 214′.

Next, a design method for the modulated optical-waveguide core widths inthe mode coupling means 212 and the mode re-coupling means 213 shown inFIG. 7 will be described with reference to FIG. 11. The modulated corewidth of the optical waveguide is determined by applying the fundamentalconcept of a wave transmission medium. Here, the “wave” which ispropagated through the wave transmission medium is “light” because ofthe application to the lightwave circuit. A theory concerning the wavetransmission medium designates the characteristic of the medium on thebasis of a general wave equation, and it can, in principle, hold true ofa general wave.

Since the use of symbols is more convenient for describing the designmethod for the modulated core width of the optical waveguide, thesymbols as stated below shall be employed for representing variousquantities. Incidentally, since the light (field) to be handled is notrestricted to light in a single state, light in each individual stateshall be generally represented by applying an index j, in order thatlight in which lights in a plurality of states are superposed may behandleable. In the ensuing description, the coordinate axis of thepropagation direction of the light will be assumed the z-axis (z=0corresponds to a plane of incidence, while z=z_(e) corresponds to aplane of emergence), and a coordinate axis in a lateral directionrelative to the propagation direction of the light will be assumed anx-axis.

ψ^(j)(x): jth incident field (which is a complex vector value function,and which is stipulated by an intensity distribution and a phasedistribution to be set at the plane of incidence, and wavelengths andpolarizations)

Φ^(j)(x): jth emergent field (which is a complex vector value function,and which is stipulated by an intensity distribution and a phasedistribution to be set at the plane of emergence, and wavelengths andpolarizations)

Incidentally, unless intensity amplification, wavelength conversion andpolarization conversion are performed in the lightwave circuit, thesummation of the light intensities of ψ^(j)(x) and Φ^(j)(x) is the same(or is attended with a negligible loss), and the wavelengths andpolarizations of these fields are the same.

{ψ^(j)(x), Φ^(j)(x)}: input/output pair (set of input/output fields)

{ψ^(j)(x), Φ^(j)(x)} is stipulated by the intensity distributions andphase distributions at the plane of incidence and the plane ofemergence, and the wavelengths and the polarizations.

{n_(q)}: refractive index distribution (set of the values of the wholelightwave-circuit design region)

When one refractive index distribution is given to the given incidentfield and emergent field, the field of light is determined, and hence,it is necessary to consider a field for all refractive indices given bythe qth iterative calculation. Therefore, the whole refractive indexdistribution may well be represented as n_(q)(x, z) where (x, z) denotesan indeterminate variable, but it shall be represented as {n_(q)} inorder to distinguish it from the value n_(q)(x, z) of a refractive indexin a place (x, z).

n_(core): symbol which indicates the value of a high refractive indexrelative to surrounding refractive indices, as at a core part in theoptical waveguide

N_(clad): symbol which indicates the value of a low refractive indexrelative to n_(core), as at a clad part in the optical waveguide

ψ^(j)(z, x, {n_(q)}): value of a field in the place (x, z) in the casewhere the jth incident field ψ^(j)(x) has been propagated to z withinthe refractive index distribution {n_(q)}

Φ^(j)(z, x, {n_(q)}): value of a field in the place (x, z) in the casewhere the jth emergent field Φ^(j)(x) has been propagated backwards to zwithin the refractive index distribution {n_(q)}

In this embodiment, {n_(q)} is given so that the core width of theoptical waveguide may become Φ^(j)(Z_(e), x, {n_(q)})=Φ^(j)(x) for allj's, or a state close thereto. An “input port” and an “output port” are“regions” where fields are concentrated at an incident end face and anemergent end face, respectively. By way of example, they are regionswhere light intensities can be propagated to optical fibers byconnecting the fibers to the corresponding parts. Here, the intensitydistributions and phase distributions of fields can be designed so as todiffer between the jth and kth ones, so that a plurality of ports can beprovided at each of the incident end face and emergent end face.

Further, in a case where the set of the incident field and emergentfield is considered, a phase which is developed by the propagationbetween the fields differs depending upon the frequency of light.Regarding lights of different frequencies (that is, lights of differentwavelengths), therefore, different ports can be set irrespective ofwhether field shapes including phases are the same or orthogonal. Here,an electromagnetic field is a field of real-number vector value, and ithas a wavelength and a polarized state as parameters, but the values ofits components shall be indicated by a complex number easy of generalmathematical handling, and the solution of an electromagnetic wave shallbe represented by the complex number.

Besides, it is assumed in the ensuing computations that the intensity ofthe whole field is normalized to 1 (one). For the jth incident fieldψ^(j)(x) and emergent field Φ^(j)(x), a propagation field and a backwardpropagation field shall be represented as ψ^(j)(z, x, {n}) and Φ^(j)(z,x, {n}) as the complex vector value functions of each place. The valuesof these functions change depending upon the refractive indexdistribution {n}, and therefore have the refractive index distribution{n} as a parameter.

ψ^(j)(x)=ψ^(j)(0, x, {n}) and Φ^(j)(x)=Φ^(j)(z_(e), x, {n}) hold good inaccordance with the definitions of the symbols. The values of thesefunctions can be easily computed by a known technique such as beampropagation method, when the incident field ψ^(j)(x), emergent fieldΦ^(j)(x) and refractive index distribution {n} are given.

An algorithm for determining a spatial refractive index distributionwill be described below. Shown in FIG. 11 is a computation procedure fordetermining the spatial refractive index distribution of a wavetransmission medium. Since the computations are iteratively executed,the number of times of the iterations is indicated by q, and thesituation of the qth computation after the computations up to the(q−1)th one have been executed is illustrated.

The propagation field and the backward propagation field are evaluatedby numerical computations for the jth incident field ψ^(j)(x) andemergent field Φ^(j)(x), on the basis of the refractive indexdistribution {n_(q-1)} obtained by the (q−1)th computation, and theresults are respectively represented as ψ^(j)(z, x, {n_(q-1)}) andΦ^(j)(z, x, {n_(q-1)}) (step S22). On the basis of these results, therefractive index n_(q)(z, x) in each place (z, x) is evaluated by thefollowing formula (step S24):n _(q)(z,x)=n _(q-1)−αΣ_(j) Im[φ ^(j)(z,x,{n _(q-1)})*·ψ^(j)(z,x,{n_(q-1)})]  (1)

Here, symbol “·” in the second term of the right side signifies an innerproduct calculation, and “Im[ ]” signifies the imaginary part of theresult of the field inner-product calculation within [ ]. Incidentally,symbol “*” denotes a complex conjugate. A coefficient α has a valueobtained in such a way that a value smaller than several tenths ofn_(q)(z, x) is further divided by the number of the sets of fields.“Σ_(j)” signifies to take a sum for the indices j's. The steps S22 andS24 are iterated, and the computation is ended when the absolute valueof the difference between the value Ψ^(j)(z_(e), x, {n}) and theemergent field Φ^(j)(x) at the emergent plane of the propagation fieldhas become smaller than a desired error d_(j) (step S23: YES).Incidentally, at a step S21, “q←(q+1)” signifies that a value with 1(one) added to the value of the present q is set as a new q.

In the above computations, the initial values {n_(o)} of the refractiveindex distribution may be appropriately set, but when the initial values{n_(o)} are close to an expected refractive index distribution, theconvergence of the computations quickens to that extent (step S20).Besides, in computing Φ_(j)(z, x, {n_(q-1)}) and Ψ^(j)(z, x, {n_(q-1)})for individual j's, a computer capable of computations in parallel maycompute for the respective j's (that is, for the respective Φ^(j)(z, x,{n_(q-1)})'s and Ψ^(j)(z, x, {n_(q-1)})'s), and hence, the computationscan be made efficient by employing a cluster system or the like (stepS22). Besides, in a case where a computer is configured having acomparatively small memory, it is also possible to select appropriatej's for individual q's in the part of the sum for the indices j's inFormula (1), to compute only Φ^(j)(z, x, {n_(q-1)})'s and Ψ^(j)(z, x,{n_(q-1)})'s of the corresponding parts and to iterate the subsequentcomputation (step S22). In a case where the values of Φ_(j)(z, x,{n_(q-1)}) and Ψ^(j)(z, x, {n_(q-1)}) are close in the abovecalculation,Im[Φ^(j)(z,x,{n_(q-1)})*·Ψ^(j)(z,x,{n_(q-1)}))]in Formula (1) becomes a value corresponding to a phase difference, anda desired output can be obtained by decreasing this value. That is, indetermining the core width of the optical waveguide, the core width maybe enlarged or reduced so that the value ofIm[Φ^(j)(z,x,{n_(q-1)})*·Ψ^(j)(z,x,{n_(q-1)})]may become smaller at the interface between the core and the clad in therefractive index distribution of the (q−1)th computed result.

The above calculation contents for determining the core width of theoptical waveguide are summarized as stated below. Ψ is let denote afield (forward propagating light) which is developed in such a way thatthe field of signal light inputted from the input port of the inputoptical waveguide 211 is propagated from the side of the input opticalwaveguide 211 onto the side of the output optical waveguide 214, whileΦ* is let denote a field (backward propagating light) which is developedin such a way that a field obtained by inverting the phase of the fieldof desired signal light outputted from the desired output port of theoutput optical waveguide 214 is propagated from the side of the outputoptical waveguide 214 onto the side of the input optical waveguide 211.On this occasion, when the z-axis shown in FIG. 7 gives a refractiveindex distribution in which the phase difference between the forwardpropagating light Ψ and the backward propagating light Φ* is minimizedat each position, an optimal lightwave circuit for converting theinputted signal light into desired output signal light can beconfigured. Concretely, the phase difference (Ψ−Φ*) of the forwardpropagating light and the backward propagating light at the interfacebetween the core and the clad is computed at each position of the z-axisshown in FIG. 7. In a case where the phase difference of the forwardpropagating light and the backward propagating light at the interfacebetween the core and the clad is positive (Ψ−Φ*>0), the phase differenceof Ψ and Φ* can be minimized by enlarging the core width of the opticalwaveguide. On the other hand, in a case where the phase difference ofthe forward propagating light and the backward propagating light at theinterface between the core and the clad is negative (Ψ−Φ*<0), the phasedifference of Ψ and Φ* can be minimized by reducing the core width ofthe optical waveguide. The optimal lightwave circuit can be configuredin such a way that, on the basis of such a design method, the opticalwaveguide widths which minimize the phase differences of the forwardpropagating light Ψ and the backward propagating light Φ* at theindividual positions of the z-axis are respectively evaluated bycomputations.

Here, in a case where the change of the optical waveguide width isabrupt relative to the signal-light propagation direction, there occursthe problem that the fabrication of the lightwave circuit becomesdifficult. Accordingly, the variation of the core width of the opticalwaveguide should desirably be continuous and smooth and lie within arange of ±8.0 μm per unit length (1 μm) in the signal-light propagationdirection in consideration of the wavelength of the signal light.Further, satisfactory effects are attained even when the variation islimited within a range of ±4.0 μm.

Next, the design of the optical-waveguide crossing portion 215 will bedescribed. Regarding the core width of the optical waveguide of theoptical-waveguide crossing portion 215, the core width w2 of the opticalwaveguide at the position (z=z2) between the end (z=z1) of theoptical-waveguide crossing portion 215 on the side of the input opticalwaveguides 211 and the central part (z=z3) of the optical-waveguidecrossing portion 215 is made larger than the core width w1 of theoptical waveguide at the end (z=z1) of the optical-waveguide crossingportion 215 on the side of the input optical waveguides 211 and the corewidth w3 of the optical waveguide at the central part (z=z3) of theoptical-waveguide crossing portion 215 (that is, w1<w2 and w2>w3), andthe core width w4 of the optical waveguide at the position (z=z4)between the central part (z=z3) of the optical-waveguide crossingportion 215 and the end (z=z5) of the optical-waveguide crossing portion215 on the side of the output optical waveguides 214 is made larger thanthe core width w3 of the optical waveguide at the central part (z=z3) ofthe optical-waveguide crossing portion 215 and the core width w5 of theoptical waveguide at the end (z=z5) of the optical-waveguide crossingportion 215 on the side of the output optical waveguides 214 (that is,w3<w4 and w4>w5).

Owing to such a configuration, there is brought forth the advantage thatthe higher-order mode and radiation mode of the signal light propagatingthrough the optical-waveguide crossing portion 215 are avoided frombeing outputted from the output optical waveguide 214 except the desiredoutput port, and a crosstalk characteristic in the crossing portion canbe greatly improved.

The planar lightwave circuit shown in FIG. 7 can be fabricated by aprocedure as stated below. An under cladding layer of SiO₂ is firstdeposited on an Si substrate by flame hydrolysis deposition or the like,and a core layer of SiO₂ glass which is doped with GeO₂ as a dopant issubsequently deposited. Next, the core layer is etched by employing apattern based on the above design as shown in FIG. 7, thereby tofabricate an optical waveguide portion. Lastly, an over cladding layerof SiO₂ is deposited again.

The planar lightwave circuit shown in FIG. 7 has been designed with theupper limit of the variation width of the core width of the opticalwaveguide set at +4.0 μm per unit length (1 μm) in the signal-lightpropagation direction. The widths of the cores of the input waveguidesand output waveguides are 7 μm. The thickness of the core of thewaveguide within the planar lightwave circuit is 6 μm.

The z-axial lengths of the mode coupling means 212 and mode re-couplingmeans 213 are in the order of 100 μm. Since, however, the z-axiallengths of the mode coupling means 212 and mode re-coupling means 213depend upon the crossing angle 216, they are not strictly determined.

The planar lightwave circuit shown in FIG. 8 is another planar lightwavecircuit in this embodiment, and it differs from the planar lightwavecircuit shown in FIG. 7, in the point that the upper limit of thevariation width of the core width of an optical waveguide has beendesigned as ±8.0 μm per unit length (1 μm) in a signal-light propagationdirection.

By the way, in the case where the core width of the optical waveguidehas been varied, a place where the waveguide partly becomes null issometimes included with the variation of the core width. That is, theplanar lightwave circuit in this embodiment has sometimes the modecoupling means 212 and the mode re-coupling means 213 configured of theoptical waveguides whose core widths partly become zero, and advantagesto be described below can be attained even in such a configuration.

Shown in FIG. 9 are the wavelength-dependencies of the propagationlosses of signal light in the planar lightwave circuit of the fourthembodiment according to the invention and the cross waveguide of theprior-art example. Regarding the planar lightwave circuit of the fourthembodiment according to the invention, the wavelength-dependencyproperties of the propagation loss of the signal light was obtained inthe planar lightwave circuit configured in such a way that the variationof the core width of the optical waveguide in the mode coupling means aswell as the mode re-coupling means was limited within the range of ±8.0μm per unit length (1 μm) in the signal-light propagation direction.Incidentally, the crossing angle of the cross waveguide was 100. It isseen from FIG. 9 that the propagation loss of the signal light has beenlowered to about 0.1 dB in a wavelength band of 1300-1600 nm.

In this manner, even in the case where the variation of the opticalwaveguide width has been limited within the range of ±8.0 μm per 1 μm indesign, the sufficient effect of lowering the optical coupling loss isattained. Besides, although the result in the case of the crossing angleof 10° is shown in FIG. 9, the effect of lowering the optical couplingloss becomes greater as the crossing angle is smaller.

Shown in FIG. 10 are the wavelength-dependencies of the crosstalkcharacteristics of the planar lightwave circuit of the fourth embodimentaccording to the invention and the cross waveguide of the prior-artexample. Regarding the planar lightwave circuit of the fourth embodimentaccording to the invention, the wavelength-dependency properties of thecrosstalk characteristic of the cross waveguide was obtained in theplanar lightwave circuit configured in such a way that the variation ofthe core width of the optical waveguide in the mode coupling means aswell as the mode re-coupling means was limited within the range of ±8.0μm per unit length (1 μm) in the signal-light propagation direction.Incidentally, the crossing angle of the cross waveguide was 10°.

It is seen from FIG. 10 that the crosstalk has been improved to about45-49 dB in a wavelength band of 1300-1600 nm. In this manner, even inthe case where the variation of the optical waveguide width has beenlimited within the range of ±8.0 μm per 1 μm in design, the sufficientlyfavorable crosstalk characteristic is attained. Besides, although theresult in the case of the crossing angle of 10° is shown in FIG. 10, aneffect on the enhancement of the crosstalk characteristic becomesgreater as the crossing angle is smaller. Concretely, it has beenverified that, also in a case where the crossing angle is 3°, asufficient effect of lowering the optical coupling loss is attained.

Further, in this embodiment, even in a case where the crossing angle is90° or wider, a sufficient effect of lowering the optical coupling losscan be attained. In a case, for example, where the crossing angle 216 isset at 150°-177° (that is, the supplementary angle of the crossing angle216 is set at 3°-30°) in FIG. 7 or FIG. 8, a sufficient effect oflowering the optical coupling loss can be attained as in a case wherethe crossing angle 216 is set at 3°-30°.

As described above, in the prior-art cross waveguide, in the case wherethe crossing angle is 30° or narrower, the optical coupling loss in thecrossing portion is high, and the crosstalk characteristic is inferior,whereas with the invention, even in the case where the crossing angle is30° or narrower, the optical coupling loss can be lowered, and thecrosstalk characteristic can be improved. Although this is notrestrictive, the invention can provide the planar lightwave circuithaving the cross waveguide whose crossing angle lies in, for example,the range of 3-30° or 150°-177°.

Fifth Embodiment

Next, the fifth embodiment will be described with reference to FIGS. 12and 13.

FIG. 12 is a plan view in which a crossing planar lightwave circuit inthe fifth embodiment according to the present invention is seen in adirection perpendicular to a substrate. Here, the cross waveguide issupposed in FIG. 12, and this is because the planar lightwave circuitaccording to the invention functions for the lowering of a crossing lossvery effectively. However, the planar lightwave circuit according to theinvention is not restricted to this embodiment, but it can be configuredas a planar lightwave circuit having another function, such as opticalmultiplexing/demultiplexing.

As shown in FIG. 12, the cross waveguide (planar lightwave circuit)according to the fifth embodiment is configured of two input opticalwaveguides 111, mode coupling means 112 for coupling part of signallight inputted to the input optical waveguide 111, to a higher-ordermode and a radiation mode, mode re-coupling means 113 for re-couplingthe higher-order mode and the radiation mode optically coupled in themode coupling means 112, to output signal light in consideration ofphases, two output optical waveguides 114 which output the output signallight optically re-coupled in the mode re-coupling means 113, and one ormore insular core portions 141 which have refractive indices equal tothe refractive index of a core.

The mode coupling means 112 and the mode re-coupling means 113 areconfigured of optical waveguides whose widths are varied aperiodicallysmoothly.

Besides, as shown in FIG. 12, in the cross waveguide (planar lightwavecircuit) according to the fifth embodiment, not only the widths of thecores of the optical waveguides are varied, but also one or more insularcore portions 141 equal in the refractive index to the cores can becaused to exist sporadically at parts outside those cores of the opticalwaveguides in which the phase difference between Ψ and Φ* is minimized.Further, a portion where the width of the core of the waveguide becomeszero (disappears) can be caused to exist.

Here, Ψ and Φ* denote a field (forward propagating light) which isdeveloped in such a way that the field of the signal light inputted fromthe input optical waveguide 111 is propagated from the side of the inputoptical waveguide 111 onto the side of the output optical waveguide 114,and a field (backward propagating light) which is developed in such away that a field obtained by inverting the phase of the field of desiredsignal light outputted from the output optical waveguide 114 ispropagated from the side of the output optical waveguide 114 onto theside of the input optical waveguide 111, respectively.

The modulated core widths of the optical waveguides of the crossingplanar lightwave circuit shown in FIG. 12 can be formed by employing theformation method described in the first embodiment.

In this case, in comparison with the case of a configuration which doesnot include the insular core portions 141, a propagation loss in thecase where a signal light wavelength is 1550 nm is greatly improved from0.3 dB to 0.1 dB.

However, in a case where the sizes of the insular core portions 141equal in the refractive index to the cores are small, there is involvedthe problem that the fabrication of the planar lightwave circuit becomesdifficult. Moreover, in a case where the sizes are excessively small,the signal light passes through the insular core portions, and hence,the improvement of the characteristics of the planar lightwave circuitcannot be expected. Accordingly, the length of one side of each insularcore portion 141 equal in the refractive index to the core needs to bemade greater than about 1/10 of the wavelength of the signal light andless than about 1 μm in order that the characteristic of the planarlightwave circuit which is fabricated by employing the existingfabrication process may be enhanced by the above configuration. In acase, for example, where the wavelength of the signal light is 1.55 μm,the length of one side of each insular core portion 141 needs to beabout 0.15 μm. Also when such a condition is attached, a sufficientlyfavorable characteristic can be attained.

FIG. 13 shows the wavelength-dependency properties of the propagationloss of signal light inputted to one port of the input opticalwaveguides 111, in the case where the planar lightwave circuit accordingto the invention has been fabricated as the cross waveguide. It is seenfrom FIG. 13 that the propagation loss of the signal light has beenlowered to about 0.1 dB in a wavelength band of 1300-1600 nm.

Sixth Embodiment

Next, the sixth embodiment according to the present invention will bedescribed with reference to FIG. 14.

A cross waveguide (planar lightwave circuit) according to the sixthembodiment is a modification to the cross waveguide (planar lightwavecircuit) according to the fifth embodiment.

FIG. 14 is a plan view in which a cross waveguide (planar lightwavecircuit) according to the sixth embodiment is seen in a directionperpendicular to a substrate. Here, the cross waveguide is supposed inFIG. 14, and this is because the planar lightwave circuit according tothe invention functions for the lowering of a crossing loss veryeffectively. However, the planar lightwave circuit according to theinvention is not restricted to this example, but it can be configured asa planar lightwave circuit having another function, such as opticalmultiplexing/demultiplexing.

The crossing planar lightwave circuit shown in FIG. 14 is configured oftwo input optical waveguides 111, mode coupling means 112 for couplingpart of a signal inputted to the input optical waveguide 111, to ahigher-order mode and a radiation mode, mode re-coupling means 113 forre-coupling the higher-order mode and the radiation mode opticallycoupled in the mode coupling means 112, to output signal light inconsideration of phases, two output optical waveguides 114 which outputthe output signal light optically re-coupled in the mode re-couplingmeans 113, one or more insular core portions 141 which have refractiveindices equal to the refractive index of a core, and one or more insularclad portions 161 which have refractive indices equal to the refractiveindex of a clad.

Besides, as shown in FIG. 14, in the crossing planar lightwave circuitaccording to the sixth embodiment, not only the widths of the cores ofthe optical waveguides are varied, but also one or more insular cladportions 161 equal in the refractive index to the clads can be caused toexist sporadically inside those cores of the optical waveguides in whichthe above phase difference between ψ and Φ* is minimized.

Here, Ψ and Φ* denote a field which is developed in such a way that thefield of signal light inputted from the input optical waveguide 111 ispropagated in a forward direction from the side of the input opticalwaveguide 111, and a field which is developed in such a way that a fieldobtained by inverting the phase of the field of desired signal lightoutputted from the output optical waveguide 114 is propagated in abackward direction from the side of the output optical waveguide 114,respectively.

In this case, in comparison with the case of a configuration which doesnot include the insular clad portions 161, a propagation loss in thecase where a signal light wavelength is 1550 nm is greatly improved from0.3 dB to 0.07 dB.

The modulated core widths of the optical waveguides of the crossingplanar lightwave circuit shown in FIG. 14 can be formed by employing theformation method described in the first embodiment.

However, in a case where the sizes of the insular clad portions 161equal in the refractive index to the clads are small, there is involvedthe problem that the fabrication of the planar lightwave circuit becomesdifficult. Moreover, in a case where the sizes are excessively small,the signal light passes through the insular clad portions, and hence,the improvement of the characteristics of the planar lightwave circuitcannot be expected. Accordingly, the length of one side of each insularclad portion 161 equal in the refractive index to the clad needs to bemade greater than about 1/10 of the wavelength of the signal light andless than about 1 μm in order that the characteristic of the planarlightwave circuit which is fabricated by employing the existingfabrication process may be improved by the above configuration. Alsowhen such a condition is attached, a sufficiently favorablecharacteristic can be attained.

Incidentally, although one or more insular core portions 141 equal inthe refractive index to the cores and one or more insulator cladportions 161 equal in the refractive index to the clads are respectivelyexistent in FIG. 14, they need not exist simultaneously, but aconfiguration in which only one or more insular clad portions 161 equalin the refractive index to the clads are existent may well be employed.

Seventh Embodiment

The seventh embodiment according to the present invention will bedescribed with reference to FIGS. 15 through 18.

FIG. 15 is a plan view in which an optical branch circuit (planarlightwave circuit) in the seventh embodiment according to the inventionis seen in a direction perpendicular to a substrate. A z-axis indicatesthe propagation direction of signal light. As shown in FIG. 15, theoptical branch circuit according to the seventh embodiment is configuredof one input optical waveguide 311 to which the signal light isinputted, mode coupling means 312 for coupling part of the signal lightinputted to the input optical waveguide 311, to a higher-order mode or aradiation mode, mode re-coupling means 313 for re-coupling thehigh-order mode or radiation mode optically coupled to the mode couplingmeans 312, in consideration of phases, at least two branching opticalwaveguides 314 a and 314 b which branches the signal light opticalcoupled to the mode re-coupling means 313, and at least two outputoptical waveguides 315 a and 315 b which output the signal lightoptically coupled to the branching optical waveguides 314 a and 314 b.Besides, in this embodiment, a crossing angle which is defined betweentwo straight lines passing through the respective centers of the twooutput optical waveguides 315 a and 315 b, in a case where the twostraight lines are extended onto the side of the input optical waveguide311, is set as the branching angle 316 of the optical branch circuit. Inaddition, “w1” indicates the minimum interval between the branchingoptical waveguides 314 a and 314 b which adjoin along the signal-lightpropagation direction in the mode re-coupling means 313.

The input optical waveguide 311 and the two output optical waveguides315 a and 315 b are respectively connected to optical fibers which existoutside the optical branch circuit according to the invention. The modecoupling means 312 is configured of an optical waveguide which iscontinuous from the input waveguide 311, and it is further connectedcontinuously to an optical waveguide in the mode re-coupling means 313.Besides, the optical waveguide in the mode re-coupling means 313 isbranched midway, thereby to configure the two or more branching opticalwaveguides 314 a and 314 b. The branching optical waveguides 314 a and314 b are continuously connected to the output optical waveguides 315 aand 315 b in the propagation direction of the signal light,respectively. Incidentally, regarding the mode coupling action and themode re-coupling action, the actions fulfilled by the mode couplingmeans and the mode re-coupling means change continuously in the vicinityof the boundary part between these means, and hence, the boundary is notdefinitely defined between the mode coupling means 312 and the modere-coupling means 313. In FIG. 15, accordingly, the mode coupling means312 and the mode re-coupling means 313 is illustrated overlappingpartly.

In the invention, the optical waveguides in the mode coupling means 312and the mode re-coupling means 313 are configured so as to have theircore widths varied aperiodically, respectively. That is, the inventionis characterized in that the optical waveguides of individual portionswithin an optical branch circuit are not configured only of the straightlines and curves of constant core widths as in the prior-art technique,but that the core widths of the optical waveguides are aperiodicallyvaried. In the optical branch circuit according to the prior-arttechnique, the optical waveguide has been configured of only a simpleshape such as a straight line, a curve or a taper, for the constant corewidth in order to suppress the development of the higher-order modecausing the variation of a branching ratio. In contrast, the opticalbranch circuit according to the invention is characterized in that thecore width is aperiodically varied, whereby the higher-order mode havingbeen avoided in the prior art is daringly developed and is thereafterre-coupled. That is, as will be described in detail later, the corewidth of the optical waveguide as is aperiodically varied is evaluatedby iterative calculations based on a computer, whereby the shape of acircuit element is designed separately from the existing element shapesuch as the straight line, curve or taper. Thus, it is possible torealize the optical branch circuit whose optical coupling loss is low,whose branching ratio is stable, and which is much smaller than theprior-art optical branch circuit.

Now, a design method for the optical-waveguide core widths variedaperiodically, in the mode coupling means 312 and the mode re-couplingmeans 313 shown in FIG. 15 will be described with reference to FIG. 18.The modulated core width of the optical waveguide is determined byapplying the fundamental concept of a wave transmission medium. Here,the “wave” which is propagated through the wave transmission medium is“light” because the fundamental concept of the wave transmission mediumis applied to the lightwave circuit. A theory concerning the wavetransmission medium designates the characteristic of the medium on thebasis of a general wave equation, and it can, in principle, hold true ofa general wave. Since the use of symbols becomes clearer for describingthe design method for the modulated core width of the optical waveguide,the symbols as stated below shall be employed for representing variousquantities.

Incidentally, the light (field) to be handled in the design of thebranch circuit of the invention is not restricted to light in a singlestate. Therefore, light in each individual state shall be generallyrepresented by applying an index j, in order that light in which lightsin a plurality of states are superposed may be handleable. In theensuing description, as shown in FIG. 15, the coordinate axis of thepropagation direction of the light will be assumed the z-axis (z=0corresponds to a plane of incidence, while z=z_(e) corresponds to aplane of emergence), and a coordinate axis in a direction which isperpendicular to the propagation direction of the light and which isparallel to the formation surface of the optical branch circuit will beassumed an x-axis.

ψ^(j)(x): jth incident field (which is a complex vector value function,and which is stipulated by an intensity distribution and a phasedistribution to be set at the plane of incidence (z=0), and wavelengthsand polarizations)

φ^(j)(x): jth emergent field (which is a complex vector value function,and which is stipulated by an intensity distribution and a phasedistribution to be set at the plane of emergence (z=z_(e)), andwavelengths and polarizations)

Incidentally, unless intensity amplification, wavelength conversion andpolarization conversion are performed in the lightwave circuit, thesummation of the light intensities of ψ^(j)(x) and φ^(j)(x) is the same(or is attended with a negligible loss), and the wavelengths andpolarizations of ψ^(j)(x) and φ^(j)(x) are the same.

{ψ^(j)(x), φ^(j)(x)}: input/output pair (set of input/output fields)

{ψ^(j)(x), φ^(j)(x)} is stipulated by the intensity distributions andphase distributions at the plane of incidence and the plane ofemergence, and the wavelengths and the polarizations.

{n_(q)}: refractive index distribution (set of the values of the wholelightwave-circuit design region)

When one refractive index distribution is given to the given incidentfield and emergent field, the field of light is determined, and hence,it is necessary to consider a field for the whole refractive indexdistribution given by the qth iterative calculation. Therefore, thewhole refractive index distribution may well be represented as n_(q)(z,x) where (z, x) denotes an indeterminate variable, but it shall berepresented as {n_(q)} in order to distinguish it from the valuen_(q)(z, x) of a refractive index in a place (z, x).

ψ^(j)(Z, x, {n_(q)}): Field value in the place (z, x), in the case wherethe jth incident field ψ^(j)(x) has been propagated to z in therefractive index distribution {n_(q)}.

φ^(j)(z, x, {n_(q)}): Field value in the place (z, x), in the case wherethe jth emergent field φ^(j)(x) has been propagated backwards to z inthe refractive index distribution {n_(q)}.

In this embodiment, the refractive index distribution {n_(q)} is givenso that the core width of the optical waveguide may become ψ^(j)(z_(e),x, {n_(q)})=φ^(j)(x) for all j's, or a state close thereto. An “inputport” and an “output port” are regions where fields are concentrated atan incident end face (z=0) and an emergent end face (z=z_(e)),respectively. By way of example, they are regions where lightintensities can be propagated to optical fibers by connecting the fibersto the corresponding parts. Here, the intensity distributions and phasedistributions of fields can be designed so as to differ between the jthand kth ones, so that a plurality of ports can be provided at each ofthe incident end face and emergent end face. Further, in a case wherethe set of the incident field and emergent field is considered, a phasedifference which is developed by the propagation between the incidentend face and the emergent end face differs depending upon the frequencyof light. Regarding lights of different frequencies (that is, lights ofdifferent wavelengths), therefore, different ports can be setirrespective of whether field shapes including phases are the same ororthogonal.

Here, an electromagnetic field is a field of real-number vector value,and it has a wavelength and a polarized state as parameters, but thevalues of its components shall be indicated by a complex number easy ofgeneral mathematical handling, and the solution of an electromagneticwave shall be represented by the complex number. Besides, it is assumedin the ensuing computations that the intensity of the whole field isnormalized to 1 (one).

For the jth incident field ψ^(j)(x) and emergent field φ^(j)(x), apropagation field and a backward propagation field shall be representedas ψ^(j)(z, x, {n}) and φ^(j)(z, x, {n}) as the complex vector valuefunctions of each place. The values of these functions change dependingupon the refractive index distribution {n}, and therefore have therefractive index distribution {n} as a parameter. ψ^(j)(x)=ψ^(j)(0, x,{n}) and φ^(j)(x)=φ^(j)(z_(e), x, {n}) hold good in accordance with thedefinitions of the symbols. The values of these functions can be easilycomputed by a known technique such as beam propagation method, when theincident field ψ^(j)(x), emergent field φ^(j)(x) and refractive indexdistribution {n} are given. An algorithm for determining a spatialrefractive index distribution will be described below.

FIG. 18 shows a computation procedure for determining the spatialrefractive index distribution of a wave transmission medium. Since thecomputations are iteratively executed, the number of times of theiterations is indicated by q, and the situation of the qth computationafter the computations up to the (q−1)th one have been executed isillustrated in the computation procedure of FIG. 18. The propagationfield and the backward propagation field are evaluated by numericalcomputations for the jth incident field ψ^(j)(x) and emergent fieldφ^(j)(x), on the basis of the refractive index distribution {n_(q-1)}obtained by the (q−1)th computation, and the results are respectivelyrepresented as ψ^(j)(z, x, {n_(q-1)}) and φ^(j)(z, x, {n_(q-1)}) (stepS32). On the basis of these results, the optical waveguide width isenlarged or reduced so as to minimize the value corresponding to thephase difference, in accordance with the refractive index n_(q)(z, x) ineach place (z, x) as is evaluated by the following formula (step S34):n _(q)(z,x)=n _(q-1)−αΣ_(j) Im[φ ^(j)(z,x,{n _(q-1)})*·ψ^(j)(z,x,{n_(q)})]  (1)

Here, the above formula (1) is the same as Formula (1) described inconnection with the fourth embodiment, and symbol “·” in the second termof the right side signifies an inner product calculation, while “Im[ ]”signifies the imaginary part of the result of the field inner-productcalculation within [ ]. Incidentally, symbol “*” denotes a complexconjugate. A coefficient α has a value obtained in such a way that avalue smaller than several tenths of n_(q)(z, x) is further divided bythe number of the sets of fields. “Σ_(j)” signifies to take a sum forthe indices j's. The steps S32 and S34 are iterated, and the computationis ended when the absolute value of the difference between the valueφ^(j)(z_(e), x, {n}) and the emergent field φ^(j)(x) at the emergentplane of the propagation field has become smaller than a desired errord_(j) (step S33: YES).

In the above computations, the initial values {n_(o)} of the refractiveindex distribution may be appropriately set, but when the initial values{n_(o)} are close to an expected refractive index distribution, theconvergence of the computations quickens to that extent (step S30).Besides, in computing φ^(j)(z, x, {n_(q-1)}) and Ψ^(j)(z, x, {n_(q-1)})for individual j's, a computer capable of computations in parallel maycompute for the respective j's (that is, for the respective φ^(j)(z, x,{n_(q-1)})'s and Ψ^(j)(z, x, {n_(q-1)})'s), and hence, the computationscan be made efficient by employing a cluster system or the like (stepS32). Besides, in a case where a computer is configured having acomparatively small memory, it is also possible to select appropriateindices j's from among all the indices j's to-be-handled, at eachiterative computation step q in the part of the sum for the indices j'sin Formula (1), to compute only φ^(j)(z, x, {n_(q-1)})'s and Ψ^(j)(z, x,{n_(q-1)})'s corresponding to the selected indices j's and to iteratethe subsequent computation (step S32).

In a case where the values of φ^(j)(z, x, {n_(q-1)}) and Ψ^(j)(z, x,{n_(q-1)}) are close in the above calculation, Im[φ^(j)(z, x,{n_(q-1)})*·Ψ^(j)(z, x, {n_(q-1)})] in Formula (1) becomes a valuecorresponding to the phase difference between the propagation field andthe backward propagation field. A desired output can be obtained bydecreasing the value of the phase difference. That is, in determiningthe core width of the optical waveguide, the core width may be enlargedor reduced so that the value of Im[φ^(j)(z, x, {n_(q-1)})*·Ψ^(j)(z, x,{n_(q-1)})] may become smaller at the interface between the core and theclad in the refractive index distribution of the (q−1)th computed result(step S34).

The above calculation contents based on the general wave equation in thewave transmission medium are summarized as stated below, from theviewpoint of determining the core width of the optical waveguide in theoptical branch circuit according to the invention. Ψ is let denote afield (forward propagating light) which is developed in such a way thatthe field of signal light inputted from the input port of the inputoptical waveguide 311 is propagated from the side of the input opticalwaveguide 311 onto the side of the output optical waveguide 315, whileφ* is let denote a field (backward propagating light) which is developedin such a way that a field obtained by inverting the phase of the fieldof desired signal light outputted from the desired output port of theoutput optical waveguide 315 is propagated from the side of the outputoptical waveguide 315 onto the side of the input optical waveguide 311.Here, let's consider a case where the number of the output ports of theoptical branch circuit to be designed is N. The design of the opticalbranch circuit is permitted in such a way that the desired emergentfields at the respective output ports are superposed N times inconsideration of output port positions, and that the superposed fieldsare set as the desired field at the emergent end face. On this occasion,when a refractive index distribution in which the phase differencebetween the forward propagating light Ψ and the backward propagatinglight φ* is minimized at each position of the z-axis shown in FIG. 15 isgiven, an optimal lightwave circuit for converting the inputted signallight into the desired output signal lights respectively outputted fromthe N output ports can be configured.

More concretely, the phase difference (Ψ−φ*) of the forward propagatinglight and the backward propagating light at the interface between thecore and the clad is computed at each position of the z-axis shown inFIG. 15. In a case where the phase difference of the forward propagatinglight and the backward propagating light at the interface between thecore and the clad is positive (Ψ−φ*>0), the phase difference of Ψ and φ*can be minimized by enlarging the core width of the optical waveguide.On the other hand, in a case where the phase difference of the forwardpropagating light and the backward propagating light at the interfacebetween the core and the clad is negative (Ψ−φ*<0), the phase differenceof Ψ and φ* can be minimized by reducing the core width of the opticalwaveguide.

The lightwave circuit which suppresses the scattering of the wave and inwhich the propagation loss of the signal light is low, can be designedby varying only the core width of the optical waveguide as stated above.

Here, in a case where the interval between the adjacent branchingoptical waveguides 314 a and 314 b becomes narrow due to the variationsof the core widths of these optical waveguides, there occurs the problemthat the fabrication of the lightwave circuit becomes difficult.Accordingly, the minimum value w1 of the optical-waveguide distancebetween the adjacent branching optical waveguides 314 a and 314 b shoulddesirably satisfy w1≧1.0 μm in consideration of the use of the existinglightwave-circuit fabrication process. Besides, in a case where thechange of the optical waveguide width is abrupt relative to thesignal-light propagation direction, there occurs the problem that thefabrication of the lightwave circuit becomes difficult. Accordingly, thevariation of the core width of the optical waveguide should desirably becontinuous and smooth. Further, the variation should desirably liewithin a range of ±8.0 μm per unit length (1 μm) in the signal-lightpropagation direction in consideration of the wavelength of the signallight as stated below.

In general, the wavelength of signal light for use in opticalcommunications lie in a range of 1.3-1.6 μm. Here, in a case where thevariation of an optical waveguide width is extraordinarily large incomparison with the wavelength of the signal light, the signal light isscattered in a direction perpendicular to a substrate. For this reason,the propagation loss of the signal light increases. Accordingly, thevariation magnitude of the optical waveguide width is effectively set onthe order of several times of the wavelength, concretely, within ±8.0 μmin order to excite the higher-order mode and suppress the scattering ofthe signal light as the characterizing features of the invention.Incidentally, as will be stated later, satisfactory effects are attainedeven when the variation magnitude of the core width is limited within±4.0 μm.

The optical branch circuit shown in FIG. 15 was fabricated by aprocedure as stated below. An under cladding layer of SiO₂ was firstdeposited on an Si substrate by flame hydrolysis deposition or the like,and a core layer of SiO₂ glass which was doped with GeO₂ as a dopant wassubsequently deposited. Next, the core layer was etched by employing apattern based on the above design as shown in FIG. 15, thereby tofabricate an optical waveguide portion. Lastly, an over cladding layerof SiO₂ was deposited again.

The optical branch circuit shown in FIG. 15 has been designed under theconditions that the upper limit of the variation magnitudes of the corewidths of the optical waveguides in the mode coupling means 312 and modere-coupling means 313 is set at ±4.0 μm per unit length (1 μm) in thesignal-light propagation direction, and that the minimum interval w1 ofthe adjacent optical waveguides in the branching optical waveguides 314a and 314 b is set at 1.0 μm, while the branching angle 316 is set at2.50. The widths of the cores of the input waveguide 311 and outputwaveguides 315 are 7 μm. The thickness of the core of the waveguidewithin the optical branch circuit is 6 μm. The refractive index of thecore is 1.45523, while the refractive index of the clad is 1.44428. Bythe way, in the case where the core width of the optical waveguide hasbeen varied, a place where the waveguide partly becomes null issometimes included with the variation of the core width. That is, thelightwave circuit in this embodiment is sometimes such that the modecoupling means 312 and the mode re-coupling means 313 are configured ofthe optical waveguides whose core widths partly become zero, and asufficient effect of lowering an optical coupling loss can be attainedeven in such a configuration.

FIG. 16 shows another optical branch circuit in this embodiment. Theoptical branch circuit differs from the optical branch circuit shown inFIG. 15, in the point that it includes three branching opticalwaveguides 314 a, 314 b and 314 c and output optical waveguides 315 a,315 b and 315 c. Incidentally, the cases of the two and three branchingoptical waveguides and output optical waveguides have been mentioned asthe embodiment, but it is needless to say that even a case where thenumbers of the branching optical waveguides and output opticalwaveguides are N can be performed.

FIG. 17 shows the wavelength-dependencies of the propagation losses ofsignal lights in the optical branch circuit of the seventh embodimentaccording to the invention and the optical branch circuit of theprior-art example. This corresponds to the case of designing the opticalbranch circuit under the conditions that the variation magnitudes of thecore widths of the optical waveguides in the mode coupling means 312 andmode re-coupling means 313 are limited within the range of ±4.0 μm perunit length (1 μm) in the signal-light propagation direction, and thatthe minimum interval w1 of the adjacent branching optical waveguides 314a and 314 b is limited to 1.0 μm. Incidentally, the branching angle 316of the optical branch circuit is 2.5°.

As seen from FIG. 17, the propagation loss of the signal light is about0.1 dB in a wavelength band of 1300-1600 nm, and the propagation loss issubstantially lowered as compared with that of the optical branchcircuit according to the prior-art technique. In this manner, thesufficient effect of lowering the optical coupling loss is attained evenin the case where the design condition is limited so as to bring thevariation magnitudes of the optical waveguide widths within the range of±4.0 μm per 1 μm, and where the minimum interval w1 of the adjacentbranching optical waveguides 314 a and 314 b is limited to 1.0 μm. Whenthe variation magnitudes are suppressed within ±4.0 μm, the sharplowering of the optical coupling loss can be realized by utilizing theprior-art lightwave-circuit fabrication process.

Incidentally, although the core is exemplified as being embedded in theclad, in this embodiment, the advantages of the invention can besatisfactorily attained even with a core of ridge shape.

Eighth Embodiment

Next, the eighth embodiment according to the present invention will bedescribed with reference to FIGS. 19 and 20.

FIG. 19 is a plan view in which an optical branch circuit in the eighthembodiment according to the invention is seen in a directionperpendicular to a substrate. A z-axis indicates the propagationdirection of signal light. As shown in FIG. 19, the optical branchcircuit according to the eighth embodiment is configured of an inputoptical waveguide 311, mode coupling means 312, mode re-coupling means313, at least two branching optical waveguides 314 a and 314 b, and atleast two output optical waveguides 315 a and 315 b, and the inputoptical waveguide 311, mode coupling means 312 and mode re-couplingmeans 313 is endowed with the function of removing the first-order modecontained in the signal light. The core width of each optical waveguidefurnished with the first-order mode removal function can be designed byemploying the same computation technique as that of the mode couplingmeans 312 and mode re-coupling means 313 stated in connection with theseventh embodiment. More specifically, when number “0” and number “1”are respectively assigned to the fundamental mode and the first-ordermode in the signal light inputted to the input optical waveguide 311,the core width may be enlarged or reduced in the determination of thecore width of the optical waveguide so that the value of Im[φ⁰(z, x,{n_(q-1)})*·Ψ⁰(z, x, {n_(q-1)})] may become smaller at the interfacebetween the core and the clad in the refractive index distribution ofthe (q−1)th computed result, and that the value of Im[φ¹(z, x,{n_(q-1)})*·Ψ¹(z, x, {n_(q-1)})] may become larger.

Here, in a case where the change of the optical waveguide width isabrupt relative to the signal-light propagation direction, there occursthe problem that the fabrication of the lightwave circuit becomesdifficult. Accordingly, the variation of the core width of the opticalwaveguide should desirably be continuous and smooth and lie within arange of ±8.0 μm per unit length (1 μm) in the signal-light propagationdirection in consideration of the wavelength of the signal light.Further, even when the variation is limited within ±4.0 μm, satisfactoryeffects of the invention are attained as stated below. The opticalbranch circuit shown in FIG. 19 has been fabricated by the sameprocedure as that of the optical branch circuit shown in the seventhembodiment.

FIG. 20 shows the wavelength-dependencies of the signal-lightpropagation losses in the cases where signal lights of the fundamentalmode and first-order mode of the input optical waveguide 311 wererespectively inputted as input signal lights to the optical branchcircuit of the eighth embodiment according to the invention. Thiscorresponds to the case of designing the optical branch circuit underthe condition that the variations of the core widths of the opticalwaveguides in the mode coupling means 312 and mode re-coupling means 313are limited within the range of ±4.0 μm per unit length (1 μm) in thesignal-light propagation direction. Incidentally, the branching angle316 of the optical branch circuit is 2.5°.

It is seen from FIG. 20 that, in the wavelength band of 1300-1600 nm,the propagation loss of the fundamental mode is only about 0.1 dB,whereas the propagation loss of the first-order mode is 16 dB or more.Accordingly, even when the first-order mode is contained in the inputsignal light to the optical branch circuit, it is sufficientlyattenuated by the optical waveguide including the first-order moderemoval function. Accordingly, only the fundamental mode is coupled tothe output optical waveguides 315 a and 315 b, with the result that thebranching ratio of the optical branch circuit is held constant. In thismanner, even when the design condition is limited so as to bring thevariation magnitudes of the optical waveguide widths within the range of±4.0 μm per 1 μm, the first-order mode is sufficiently attenuated, andhence, the effect of stabilizing the branching ratio of the opticalbranch circuit can be attained in spite of the use of the prior-artlightwave-circuit fabrication process.

Incidentally, although the core is exemplified as being embedded in theclad, in this embodiment, the advantages of the invention can besatisfactorily attained even with a core of ridge shape.

Ninth Embodiment

The ninth embodiment according to the present invention will bedescribed with reference to FIGS. 21 and 22.

FIG. 21 shows the structure of a slab type coupler (planar lightwavecircuit) 510 in the ninth embodiment. Three, first input opticalwaveguides 511 a, 511 b and 511 c, an optical slab waveguide 520, andfour, second input/output optical waveguides 514 a, 514 b, 514 c and 514d are arranged on a substrate. Besides, the second input/output opticalwaveguides are provided with mode coupling regions 512 each of which isbased on an optical waveguide having at least one of a core width andheight varied continuously.

Here, the slab type optical coupler of this embodiment has been realizedby silica-based optical waveguides which are formed on the siliconsubstrate. This is because the combination can provide a slab typeoptical coupler of superior reliability. However, the invention is notrestricted to this example, but any other combination may, of course, beemployed as the combination of the substrate and the optical waveguides.

Besides, the slab type optical coupler of this embodiment has beenrealized by employing the optical waveguides whose cores and cladsexhibit a relative refractive index difference of 0.3%. This is becausea slab type optical coupler of low connection losses with optical fiberscan be provided by employing the relative refractive index difference.However, the invention is not restricted to this example, but therelative refractive index difference may, of course, have another valuesuch as 0.75% or 1.5%.

Further, in the slab type optical coupler of this embodiment, the numberof the first input/output optical waveguides 511 has been set at 3, andthat of the second input/output optical waveguides 514 has been set at4, but the number of the first input optical waveguides 511 may be atleast one, and that of the second input/output optical waveguides 514may be at least 2. By way of example, the number of the firstinput/output optical waveguides 511 may well be one, and that of thesecond input/output optical waveguides 514 may well be 16 or 9.

Next, the operation of this embodiment will be described. A light signalinputted to the first input/output optical waveguide 511 is spread inthe optical slab waveguide 520, and it is turned into a plane wave whoseamplitude is in the shape of a Gaussian distribution, at the end of theoptical slab waveguide. The plane wave enters into the secondinput/output optical waveguides. In this regard, in a conventional slabtype coupler which does not have the mode coupling region, part of thelight signal is discarded as the higher-order mode or radiation mode ofthe second input/output waveguides 514 on account of the differencebetween the shapes of the plane wave and the fundamental mode of thesecond input/output optical waveguides. Here, in the slab type opticalcoupler of this embodiment, the second input/output optical waveguidesinclude the mode coupling means. Therefore, even the light signal to bediscarded in the prior art is coupled to the fundamental mode and isoutputted as the fundamental mode of the second input/output opticalwaveguides, with the result that a loss can be lowered.

FIG. 22 shows the result of the comparison of losses in the slab typeoptical coupler of this embodiment shown in FIG. 21 and the slab typeoptical coupler of the prior art. In the configuration of the prior-artslab type optical coupler, the partial signal light is discarded at theconnection points between the optical slab waveguide and the secondinput/output optical waveguides as stated above, and hence, the lossoccurs. It has been revealed, however, that the light can be branchedwith almost no loss in the slab type optical coupler of this embodiment.

Tenth Embodiment

The tenth embodiment according to the present invention will bedescribed with reference to FIGS. 23A, 23B and 23C.

Shown in FIGS. 23A, 23B and 23C is the structure of an arrayed waveguidegrating filter (planar lightwave circuit) 610 in the tenth embodimentaccording to the invention. On a substrate, there are arranged 16 inputoptical waveguides 611, a first optical slab waveguide 612 which isoptically connected to the input optical waveguides, arrayed waveguides614 which are optically connected to the optical slab waveguide, asecond optical slab waveguide 616 which is optically connected to thearrayed waveguides, and 16 output optical waveguides 617 which areoptically connected to the optical slab waveguide. Besides, modecoupling regions (FIGS. 23B and 23C) each of which is based on anoptical waveguide having at least one of a core width and height variedcontinuously are respectively disposed at the connection part 613between the arrayed waveguides 614 and the first optical slab waveguide612, and the connection part 615 between the arrayed waveguides 614 andthe second optical slab waveguide 616.

Here, the arrayed waveguide grating filter of this embodiment has beenrealized by silica-based optical waveguides which are formed on thesilicon substrate. This is because the combination can provide anarrayed waveguide grating filter of superior reliability. However, theinvention is not restricted to this example, but any other combinationmay, of course, be employed as the combination of the substrate and theoptical waveguides.

Besides, the arrayed waveguide grating filter of this embodiment hasbeen realized by employing the optical waveguides whose cores and cladsexhibit a relative refractive index difference of 0.75%. The reasontherefor is that the minimum bending radius of each optical waveguidecan be made 5 mm by employing the relative refractive index difference,so an arrayed waveguide grating filter of small size can be provided.However, the invention is not restricted to this example, but therelative refractive index difference may, of course, have another valuesuch as 0.4% or 1.5%.

Further, in the arrayed waveguide grating filter of this embodiment, thenumber of the first input/output optical waveguides 611 has been set at16, and that of the second input/output optical waveguides 617 has beenset at 16, but the number of the first input/output optical waveguides611 may be at least one, and that of the second input/output opticalwaveguides 617 may be at least 2. By way of example, the number of thefirst input/output optical waveguides 611 may well be one, and that ofthe second input/output optical waveguides 617 may well be 32 or 40.

Next, the operation of the tenth embodiment according to the inventionwill be described. A light signal inputted to the first input/outputoptical waveguide 611 is spread in the first optical slab waveguide 612,and it is turned into a plane wave whose amplitude is in the shape of aGaussian distribution, at the end of the first optical slab waveguide.The plane wave excites the arrayed optical waveguides 614. In thisregard, in a prior-art arrayed waveguide grating filter which does nothave the mode coupling region shown in FIG. 23B, part of the lightsignal is discarded as the higher-order mode or radiation mode of thearrayed waveguides on account of the difference between the shapes ofthe plane wave and the fundamental mode of the arrayed opticalwaveguides. Here, in the arrayed waveguide grating filter of thisembodiment, the arrayed optical waveguides 614 include the mode couplingregion (FIG. 23B). Therefore, even the light signal to be discarded inthe prior art is coupled to the fundamental mode and is outputted as thefundamental mode of the second input/output optical waveguides, with theresult that a loss can be lowered.

Besides, the light signal propagated through the arrayed waveguides 614is inputted to the second optical slab waveguide 616. Here, in theconventional arrayed waveguide grating filter which does not have themode coupling region, inputted light fields assume a shape in which thefundamental modes of the respective arrayed optical waveguides arearrayed, and they have a period corresponding to the pitch of thearrayed waveguides. In the light propagation in the optical slabwaveguide, an input field and an output field are in the relation ofFourier transformation. Therefore, subpeaks corresponding to the arrayedwaveguide pitches appear together with a main peak at a position atwhich the light ought to be condensed, and optical power levels led tothe subpeaks become losses. Here, in the arrayed waveguide gratingfilter of this embodiment, the arrayed optical waveguides 614 includethe mode coupling region (FIG. 23C). Therefore, light from the arrayedwaveguides 614 can be prevented from having the period corresponding tothe arrayed waveguide pitches, at the end face of the second slabwaveguide 616, with the result that the appearance of the subpeaks canbe suppressed to lower losses.

FIG. 24 shows the result of the comparison of the losses in the arrayedwaveguide grating filter of the tenth embodiment according to theinvention as shown in FIG. 23A and the arrayed waveguide grating filterof the prior art. In the configuration of the prior-art arrayedwaveguide grating filter, the partial signal light is discarded at thejunction points between the first optical slab waveguide and the arrayedwaveguide grating, and the junction points between the arrayedwaveguides and the second optical slab waveguide, as stated above, sothat the losses develop. It is seen, however, that the losses can besubstantially lowered in the arrayed waveguide grating filter of thisembodiment.

Eleventh Embodiment

The eleventh embodiment according to the present invention will bedescribed with reference to FIGS. 25 through 29.

Besides, in the ensuing embodiment, it shall be assumed that the wavepropagation direction of a wave propagation circuit is indicated by az-axis, that two axes orthogonal to the z-axis are an x-axis and ay-axis, and that the inlet position of a wave lies at z=0, while theoutlet position of the wave lies at z=L.

In addition, in this embodiment, a lightwave will be handled as thewave, and a lightwave circuit as the wave propagation circuit. This isbecause a design method for the wave propagation circuit has noessential difference for the lightwave, a microwave and a millimeterwave. Of course, the invention is not restricted to this example, butthe wave propagation circuit may well be a microwave circuit or amillimeter wave circuit.

Further, in this embodiment to be disclosed below, a planar lightwavecircuit based on silica-glass optical waveguides each of which is formedof a core of silica glass having a constant thickness and embedded in aclad layer of the silica glass will be handled as a concrete example ofthe lightwave circuit. This is because the structure can provide aprecise lightwave circuit and can provide a lightwave circuit remarkablydemonstrating the advantages of the invention. However, the invention isnot restricted to this example, but a material may well be a differentone such as polymer or semiconductor. Besides, the structure of thelightwave circuit may well be another structure which partly or whollychanges in three dimensions.

Shown in FIG. 25 is the algorithm of the design method for the wavepropagation circuit in the eleventh embodiment according to theinvention. The design method for the wave propagation circuit in thisembodiment includes the step 311 of determining the initial values of arefractive index distribution n(x, y, z) and storing the determinedvalues in the memory of a computer, the step 312 of setting an optimizedposition at a position z=z_(o) in the light propagation direction, thestep 313 of computing a field Φ(x, y, z_(o)) in the case where an inputfield Φ(x, y, 0) has propagated forwards from the inlet z=0 to theoptimized position z=z_(o), and a field Ψ(x, y, z_(o)) in the case wherea desired output field Ψ(x, y, L) has propagated backwards from theoutlet z=L to the optimized position z=z_(o), and then storing thecomputed fields in the memory of the computer, the step 314 of alteringthe refractive index distribution n(x, y, z_(o)) by the computer so thatthe wavefronts of the input field propagated forwards from the inlet tothe optimized position and the output field propagated backwards fromthe outlet to the optimized position may agree, and the step 315 ofjudging if the scanning of optimized positions has ended. The steps312-315 are iterated until the judged result of the step 315 issatisfied.

Here, in the design method for the wave propagation circuit in thisembodiment, the results of the steps 311 and 313 have been stored in thememory of the computer. This is because the method can provide atechnique which can compute at high speed by the computer. However, theinvention is not restricted to this example, but the results of thesteps 311 and 313 may well be stored in another computer-readablestorage device such as hard disk.

Next, an optimization method in the eleventh embodiment will bedescribed using formulae. The fundamental concept of a wave transmissionmedium is applied to the design method for the wave propagation circuitin the invention. A theory concerning the wave transmission mediumdesignates the characteristic of the medium on the basis of a generalwave equation, and it can, in principle, hold true of a general wave. Inthis embodiment, the “wave” which is propagated through the wavetransmission medium is “light” because of the application to thelightwave circuit.

The field Φ(x, y, z_(o)) in the case of propagating the input field Φ(x,y, 0) forwards from the inlet z=0 to the optimized position z=z_(o) asis computed at the step 313, is given by the following equation where H₁denotes a wave propagation operator from z=0 to z=z_(o):Φ(x,y,z _(o))=H ₁Φ(x,y,0)  (2)

Besides, the field Ψ(x, y, z_(o)) in the case of propagating the outputfield Ψ(x, y, L) backwards from the outlet z=L to the optimized positionz=z_(o) as is computed at the step 313, is given by the followingequation where H₂ denotes a wave propagation operator from z=z_(o) toz=L:Ψ*(x,y,z _(o))=Ψ*(x,y,L)H ₂  (3)Here, “*” represents a complex conjugate, and it indicates that theproceeding direction of the field is the backward direction.

Now, the coupling constant of the fields Φ(x, y, z_(o)) and Ψ(x, y,z_(o)) evaluated at the step 313 is represented as:∫∫ψ*(x,y,z _(o))φ(x,y,z _(o))dxdy=∫∫ψ*(x,y,L)H ₂ H ₁φ(x,y,0)dxdy  (4)Here, when it is considered that H₂H₁ denotes a wave propagationoperator from z=z_(o) to z=L, Formula (4) can be rewritten as:∫∫ψ*(x,y,L)H ₂ H ₁φ(x,y,0)dxdy=∫∫ψ*(x,y,L)φ(x,y,L)dxdy  (5)

Here, the right side of Formula (5) represents the coupling coefficientbetween the desired output field Ψ(x, y, L) and the field Φ(x, y, L)which is obtained at the outlet when the input field has been propagatedfrom the inlet. That is, when the refractive index distribution n(x, y,z_(o)) of the optimized position is modified so that the wavefronts ofboth the fields may agree, the coupling constant of the fields Φ(x, y,z_(o)) and Ψ*(x, y, z_(o)) is enhanced, and hence, the field Φ(x, y, L)which is obtained at the outlet when the input field has been propagatedfrom the inlet comes close to the desired output field Ψ(x, y, L).

In this manner, according to the design method for the wave propagationcircuit in the eleventh embodiment as shown in FIG. 25, the input fieldcan be brought close to the desired output field by altering therefractive index distribution n(x, y, z_(o)) so that the wavefronts ofthe fields Φ(x, y, z_(o)) and Ψ*(x, y, z_(o)) may agree.

With the design method for the wave propagation circuit in the eleventhembodiment, the refractive index distribution can be given asdeterminism, and hence, substantial improvement in the speed of theoptimization of the wave propagation circuit can be realized as comparedwith the optimizing speed of the cut-and-try type technique wherein therefractive index distribution is changed by way of trial, the inputfield is propagated and the judgment is made from the result.

FIG. 26 shows the initial values of the refractive index distribution ofthe lightwave circuit in the design method for the wave propagationcircuit in the eleventh embodiment. The lightwave circuit shown in FIG.26 has a structure in which a core 451 of constant film thickness isembedded in a clad layer 452. The refractive index of the clad layer 452is 1.44428, and the thickness thereof is 60 μm, while the refractiveindex of the core 451 is 1.45523, and the thickness thereof is 6 μm. Thecore 451 is configured of a rectilinear optical waveguide 453 and asectoral optical waveguide 454. The length of the rectilinear opticalwaveguide 453 is 600 μm, and the width thereof is 7 μm, while the lengthof the sectoral optical waveguide 454 is 400 μm, and the width thereofis 32 μm. The inlet of the lightwave circuit lies at z=0, and the outletthereof lies at z=L=1000 μm. Besides, in FIG. 26, the optimized positionis indicated by numeral 455.

Subsequently, the optimization of the wave propagation circuit has beenperformed in accordance with the design method for the wave propagationcircuit in the eleventh embodiment as shown in FIG. 25. Here, the inputfield has been set as the field of the fundamental mode of therectilinear optical waveguide 453, while the desired output field hasbeen set as a field in which the fundamental modes are parallel with aspacing of 18 μm, in order that the lightwave circuit may function as atwo-branch circuit. Here, although the lightwave circuit has beenoptimized so as to function as the two branches, in the design methodfor the wave propagation circuit in the eleventh embodiment, theoptimization may, of course, be performed for three branches or fourbranches, or for another function such as spot size conversion or thelowering of a waveguide crossing loss.

Besides, in this embodiment, the optimized position 455 has beenselected at random from within the sectoral region 454, and scanning hasbeen performed so as to optimize such selected optimized positions 455.The whole region from z=0 to z=L need not be scanned. However, theoptimized positions 455 may be scanned anyway, and the whole region fromz=0 to z=L may well be scanned.

Further, in the design method for the wave propagation circuit in theeleventh embodiment as shown in FIG. 25, the field computations at thestep 313 have been executed by the computer by employing a finitedifference time domain method. However, the invention is not restrictedto this example, but the field computations may, of course, be executedby employing either a beam propagation method or a mode matching method,or another computation method.

Besides, in the design method for the wave propagation circuit in theeleventh embodiment as shown in FIG. 25, the refractive indexdistribution n(x, y, z_(o)) proportional to the phase difference hasbeen given in order to bring the wavefronts into agreement, at the step314. FIGS. 27A and B show how to give the refractive index distribution.FIG. 27A shows the phase difference between the field obtained bypropagating the input field forwards and the field obtained bypropagating the desired output field backwards, while FIG. 27B shows therefractive index distribution proportional to the phase difference. Inthis manner, the coupling coefficient between the field propagatedforwards and the field propagated backwards can be enhanced by givingthe refractive index distribution which compensates for the phasedifference, with the result that the output obtained when the inputfield is inputted can be brought close to the desired field.

Here, although the refractive index distribution proportional to thephase difference has been given in the design method for the wavepropagation circuit in the eleventh embodiment as shown in FIG. 25, theinvention is not restricted to this example, but another refractiveindex distribution may, of course, be given as long as refractiveindices are given so as to bring the wavefronts into agreement at leastpartly.

Incidentally, an analog refractive index variation as shown in FIGS. 27Aand B can be realized using ultraviolet irradiation in the case of, forexample, the silica-glass optical waveguide.

FIG. 28 represents refractive-index adjustment magnitudes from theinitial values of the refractive index distribution after the wavepropagation circuit has been optimized by employing the design methodfor the wave propagation circuit in the eleventh embodiment as shown inFIG. 25. A positive part along a vertical axis in FIG. 28 is a placewhere the refractive index has been increased, whereas a negative partis a part where the refractive index has been decreased. An actualrefractive index becomes a value with the refractive index 1.45523 ofthe core added to the represented value. The refractive-index adjustmentmagnitudes shown in FIG. 28 are results which have been obtained byaltering the refractive index distribution n until the whole region fromz=0 to z=L are scanned for the optimized positions 455, by employing thedesign method for the wave propagation circuit in this embodiment.

In the case of the silica-glass optical waveguide shown in FIG. 26,however, it is difficult to decrease the refractive index. In the caseof the silica-glass optical waveguide, accordingly, the waveguide in astate before the refractive index is varied by the ultravioletirradiation is fabricated with the refractive indices of the core andthe clad equalized, and the increase of the refractive index is madesmall at the part whose refractive index is to be decreased, whereas theincrease of the refractive index is made large at the part whoserefractive index is to be increased, whereby the refractive indexdistribution as designed can be realized.

FIG. 29 shows the transmission characteristic of the wave propagationcircuit which was optimized by employing the design method for the wavepropagation circuit in the eleventh embodiment as shown in FIG. 25. Asshown in FIG. 29, it is seen that the inputted light field has beenbranched into two as designed. A loss in this case is below 0.1 dB, andit has been verified that a favorable characteristic is attained.

Twelfth Embodiment

The twelfth embodiment according to the present invention will bedescribed with reference to FIG. 30 through FIG. 34 (A and B).

Besides, in the ensuing embodiment, it shall be assumed that the wavepropagation direction of a wave propagation circuit is indicated by az-axis, that two axes orthogonal to the z-axis are an x-axis and ay-axis, and that the inlet position of a wave lies at z=0, while theoutlet position of the wave lies at z=L.

Shown in FIG. 30 is the algorithm of a design method for the wavepropagation circuit in the twelfth embodiment according to theinvention. The design method for the wave propagation circuit in thetwelfth embodiment as shown in FIG. 30 includes the step 316 ofdetermining the initial values of a refractive index distribution n(x,y, z) and storing the determined values in the memory of a computer, andsetting an optimized position at the outlet, the step 317 of computing afield distribution Φ(x, y, z) in the case where an input field Φ(x, y,0) has propagated forwards from the inlet z=0 to the outlet z=L, andthen storing the computed field distribution in the memory of thecomputer, the step 318 of propagating an output field Ψ(x, y, z)backwards a minute distance Δz in an altered refractive indexdistribution and storing the resulting distribution in the memory of thecomputer, the step 314 of altering the refractive index distribution bythe computer so that the wavefronts of the input field propagatedforwards from the inlet to the optimized position and the output fieldpropagated backwards from the outlet to the optimized position mayagree, the step 319 of shifting the optimized position onto an inletside the minute distance Δz, and the step 320 of judging if theoptimized position has arrived at the inlet, and the steps 318, 314, 319and 320 are iterated until the optimized position comes from the outletto the inlet.

Here, in the design method for the wave propagation circuit in thetwelfth embodiment as shown in FIG. 30, the results of the steps 316,317 and 318 have been stored in the memory of the computer. This isbecause the method can provide a technique which can compute at highspeed by the computer. However, the invention is not restricted to thisexample, but the results of the steps 316, 317 and 318 may, of course,be stored in another computer-readable storage device such as hard disk.

Even when such an algorithm is employed, the optimization of the wavepropagation circuit can be attained likewise to the design method forthe wave propagation circuit in the eleventh embodiment as shown in FIG.25.

Further, with the design method for the wave propagation circuit in thetwelfth embodiment as shown in FIG. 30, the fields in the case where theinput field has propagated forwards can be collectively computed andstored in the memory of the computer at the step 317, so that a stillhigher speed for the computations can be attained.

FIG. 31 shows the initial values of the refractive index distributionemployed at the step 311 of the design method for the wave propagationcircuit in the twelfth embodiment as shown in FIG. 30. As shown in FIG.31, a core 451 of constant film thickness is embedded in a clad layer452, and the core has a mosaic structure one side of which is 1 μm long.The refractive index of the clad layer 452 is 1.44428, and the thicknessthereof is 60 μm, while the refractive index of the core 451 is 1.45523,and the thickness thereof is 6 μm. The inlet of the lightwave circuitlies at z=0, and the outlet thereof lies at z=L=100 μm.

Subsequently, there will be described an example in which theoptimization of the wave propagation circuit has been performed inaccordance with the design method for the wave propagation circuit inthe twelfth embodiment as shown in FIG. 30. Here, the input field hasbeen set as the field of the fundamental mode of an optical waveguidehaving a width of 7 μm and a thickness of 6 μm, while the desired outputfield has been set so as to output the field of the fundamental mode ata position of x=20 μm for a wavelength of 1.3 μm and at a position ofx=−20 μm for a wavelength of 1.55 μm, in order that the lightwavecircuit may function as a wavelength filter. In this manner, accordingto the design method for the wave propagation circuit in the invention,a plurality of wavelengths can be employed for the desired output field.In case of employing the plurality of wavelengths, when a combinedwavefront based on the plurality of wavelengths is considered, thelightwave circuit can be designed by quite the same procedure as in thecase of one wavelength.

Incidentally, although the lightwave circuit has been optimized so as tofunction as the wavelength filter, in the design method for the wavepropagation circuit in the twelfth embodiment according to theinvention, the optimization may, of course, be performed for anotherfunction.

Besides, in the design method for the wave propagation circuit in thetwelfth embodiment as shown in FIG. 30, the field computations at thesteps 317 and 318 have been executed by the computer by employing athree-dimensional beam propagation method. However, the invention is notrestricted to this example, but the field computations may, of course,be executed by employing another technique such as a finite differencetime domain method or a mode matching method.

In addition, in the design method for the wave propagation circuit inthe twelfth embodiment as shown in FIG. 30, the step 314 has beenperformed in such a way that a threshold value T is set as O rad inorder to bring the wavefronts into agreement, and that the core isdistributed in a place whose phase difference is greater than thethreshold value, while the clad is distributed in a place whose phasedifference is smaller. FIGS. 32A and B show how to give such arefractive index distribution. In this manner, the coupling coefficientbetween the field propagated forwards and the field propagated backwardscan be enhanced by giving the refractive index distributioncorresponding to the magnitudes of the phases, with the result that theoutput obtained when the input field is inputted can be brought close tothe desired field. Further, the wave propagation circuit which is easilyfabricated by employing the two kinds of materials and the two kinds ofrefractive indices of the core and the clad layer can be provided bysuch a method of giving the refractive index distribution. However, theinvention is not restricted to this example, but it may, of course,employ a quite different method of giving the refractive indexdistribution, for example, three kinds of refractive indices are givenin accordance with the magnitudes of the phases.

In the case of giving the refractive index distribution, as the size ofthe core is larger as compared with the wavelength of the wave, thecharacteristic of the wave propagation circuit degrades more. Besides,as the size of the core becomes smaller, difficulty is involved in thefabrication of the wave propagation circuit more. Accordingly, themethod of giving the refractive index distribution in FIGS. 32A and Bhas placed the limitation that the size of the core becomes a size whichis on the order of the wavelength of the wave. That is, in thisembodiment, in consideration of the fact that the signal wavelengths areabout 1.3 μm and 1.5 μm, and in order that the size of the core maybecome on the order of the wavelength of the wave, there has been placedthe limitation that the clad layer is not distributed in a case wherethe size of the core becomes smaller than 1 μm-square. This is because awave propagation circuit easy of fabrication can be provided by thelightwave circuit configured of the clad layer and the core which has acertain larger size in this manner. Even in this way, the advantages ofthe invention can be attained. However, the invention is not restrictedto this example, but the size of the core may be a fabricable size of atleast 300 nm and may be determined in relation to the wavelength of awave to-be-inputted.

FIG. 33 shows the refractive index distribution of a wave propagationcircuit which was optimized by the design method for the wavepropagation circuit in the twelfth embodiment as shown in FIG. 30. Here,the algorithm in FIG. 30 was applied 24 times in order to obtain thewave propagation circuit in FIG. 33. In this manner, the design methodfor the wave propagation circuit in the invention can attain a favorablecharacteristic by being applied a plurality of number of times.

FIGS. 34A and B show the characteristics of a silica-made wavepropagation circuit for which a wave propagation circuit was optimizedby the design method for the wave propagation circuit in the twelfthembodiment as shown in FIG. 30, and which was fabricated by conventionalflame hydrolysis deposition on the basis of the optimization. FIG. 34Ashows the field distribution in the case where the wavelength of 1.3 μmwas inputted, while FIG. 34B shows the field distribution in the casewhere the wavelength of 1.55 μm was inputted. As shown in FIG. 33, therehas been realized the wave propagation circuit in which the lights areconcentrated at different positions, depending upon the wavelengths.

Thirteenth Embodiment

The thirteenth embodiment according to the present invention will bedescribed with reference to FIGS. 35 through 39.

Besides, in the ensuing embodiment, it shall be assumed that the wavepropagation direction of a wave propagation circuit is indicated by az-axis, that two axes orthogonal to the z-axis are an x-axis and ay-axis, and that the inlet position of a wave lies at z=0, while theoutlet position of the wave lies at z=L.

FIG. 35 shows the algorithm of a design method for the wave propagationcircuit in the thirteenth embodiment according to the invention. Thedesign method for the wave propagation circuit in the thirteenthembodiment as shown in FIG. 35 includes the step 321 of determining theinitial values of a refractive index distribution n(x, y, z) and storingthe determined values in the memory of a computer, and setting anoptimized position at the inlet, the step 322 of computing a fielddistribution Ψ(x, y, z) in the case where a desired output field Ψ(x, y,L) has propagated backwards from the outlet z=L to the inlet z=0, andthen storing the computed field distribution in the memory of thecomputer, the step 323 of propagating an input field Φ(x, y, z) forwardsa minute distance Δz in an altered refractive index distribution andstoring the resulting distribution in the memory of the computer, thestep 314 of altering the refractive index distribution by the computerso that the wavefronts of the input field propagated forwards from theinlet to the optimized position and the output field propagatedbackwards from the outlet to the optimized position may agree, the step324 of shifting the optimized position onto an outlet side the minutedistance Δz, and the step 325 of judging if the optimized position hasarrived at the inlet, and the steps 323, 314, 324 and 325 are iterateduntil the optimized position comes from the inlet to the outlet.

Here, in the design method for the wave propagation circuit in thethirteenth embodiment as shown in FIG. 35, the results of the steps 321,322 and 323 have been stored in the memory of the computer. This isbecause the method can provide a technique which can compute at highspeed by the computer. However, the invention is not restricted to thisexample, but the results of the steps 321, 322 and 323 may, of course,be stored in another computer-readable storage device such as hard disk.

Even when such an algorithm is employed, the optimization of the wavepropagation circuit can be attained likewise to the design method forthe wave propagation circuit in the eleventh embodiment as shown in FIG.25.

Further, with the design method for the wave propagation circuit in thethirteenth embodiment as shown in FIG. 35, the fields in the case wherethe output field has propagated forwards can be collectively computedand stored in the memory of the computer at the step 322, so that ahigher speed for the computations can be attained as in the designmethod for the wave propagation circuit in the twelfth embodiment of theinvention as shown in FIG. 30.

FIG. 36 shows the initial values of the refractive index distributionemployed at the step 321 of the design method for the wave propagationcircuit in the thirteenth embodiment as shown in FIG. 35. As shown inFIG. 36, a core 351 of constant film thickness is embedded in a cladlayer 352, and the refractive index of the clad layer 352 is 1.44428,and the thickness thereof is 60 μm, while the refractive index of thecore 351 is 1.45523, and the thickness thereof is 6 μm. The inlet of thelightwave circuit lies at z=0, and the outlet thereof lies at z=L=1000μm.

Subsequently, there will be described an example in which theoptimization of the wave propagation circuit has been performed inaccordance with the design method for the wave propagation circuit inthe thirteenth embodiment as shown in FIG. 35. Here, the input field hasbeen set as the field of the fundamental mode of an optical waveguidehaving a width of 7 μm and a thickness of 6 μm, while the desired outputfield has been designed in order that the lightwave circuit may functionas a waveguide lens, which forms a focus at a position being 100 μmdistant behind the output.

Incidentally, although the lightwave circuit has been optimized so as tofunction as the waveguide lens, in the design method for the wavepropagation circuit in the thirteenth embodiment of the invention, theoptimization may, of course, be performed for another function.

Besides, in the design method for the wave propagation circuit in thethirteenth embodiment as shown in FIG. 35, the field computations at thesteps 322 and 323 have been executed by the computer by employing athree-dimensional beam propagation method. However, the invention is notrestricted to this example, but the field computations may, of course,be executed by employing another technique such as a finite differencetime domain method or a mode matching method.

In addition, in the design method for the wave propagation circuit inthe thirteenth embodiment as shown in FIG. 35, the step 314 has beenperformed in such a way that a threshold value T is set as O rad inorder to bring the wavefronts into agreement, and that, regarding onlythe boundary between the core and the clad, the core is distributed (thecore is added) at a position having been the clad originally, in a placewhose phase difference is greater than the threshold value, while theclad is distributed without distributing the core (the core is removed)at a position having been the core originally, in a place whose phasedifference is smaller.

FIGS. 37A and B show how to give such a refractive index distribution.In this manner, a wave propagation circuit in which the wave isdifficult of being dispersed in up and down directions and which isfavorable in point of loss can be provided by varying the refractiveindex distribution at only the boundary between the core and the clad.However, the invention is not restricted to this example, but it may, ofcourse, employ a different method of giving the refractive indexdistribution, for example, a method which allows the distribution of aclad layer at the center of the waveguide.

Further, in the method of giving the refractive index distribution inFIGS. 37A and B, the variation rate of a core width in the lightpropagation direction has been set at 60 degrees or less. That is, themaximum inclination of the core width relative to the light propagationdirection has been set at 60 degrees or less. This is because a wavepropagation circuit in which the dispersion of the wave is still lesscan be provided by placing such a limitation. However, the invention isnot restricted to this example, but it may, of course, place thelimitation with another angle or place no limitation.

FIG. 38 shows the refractive index distribution of a wave propagationcircuit which was optimized by the design method for the wavepropagation circuit in the thirteenth embodiment as shown in FIG. 35.Here, in order to obtain the wave propagation circuit in FIG. 38, thedesign method for the wave propagation circuit in the thirteenthembodiment as shown in FIG. 35 and the design method for the wavepropagation circuit in the twelfth embodiment of the invention as shownin FIG. 30 were alternately applied 15 times. In this manner, owing tothe alternate applications, the refractive index distribution can bealtered uniformly over the whole wave propagation circuit, and afavorable characteristic can be attained. In this way, the optimizationcan be performed by the selective combination and/or iteration of thedesign methods for the wave propagation circuit in the first throughthird embodiments of the invention.

FIG. 39 shows the characteristic of a wave propagation circuit which wasoptimized by the design method for the wave propagation circuit in thethirteenth embodiment of the invention as shown in FIG. 35. FIG. 39 hasbeen obtained by measuring a loss in such a way that two pairs ofwaveguide lenses as shown in FIG. 38 were employed and that they wereopposed with a spacing of 200 μm through an optical slab waveguide. Itis seen that the favorable characteristic has been attained over a widewavelength region.

1. A planar lightwave circuit having a core and a clad which are formedon a substrate, comprising: at least one input optical waveguide whichinputs signal light; mode coupling means for coupling a fundamental modewhich is part of the inputted signal light, to at least either of ahigher-order mode and a radiation mode, or mode re-coupling means forre-coupling at least either of the higher-order mode and the radiationmode to the fundamental mode; and at least one output optical waveguidewhich outputs signal light; said mode coupling means or said modere-coupling means being an optical waveguide which has at least one of acore width and height varied irregularly continuously.
 2. A planarlightwave circuit as defined in claim 1, wherein the variation of atleast one of the core width and height of the optical waveguide iswithin ±8 μm per unit length (1 μm) in a propagation direction of thesignal light.
 3. A planar lightwave circuit as defined in claim 1,wherein said mode coupling means or said mode re-coupling means is anoptical waveguide which has at least one of the core width and heightmade zero partly.
 4. A planar lightwave circuit as defined in claim 2,wherein said mode coupling means or said mode re-coupling means is anoptical waveguide which has at least one of the core width and heightmade zero partly.
 5. A planar lightwave circuit as defined in claim 1,wherein at least one of said mode coupling means and said modere-coupling means includes at least one insular core portion which isspaced from the core of said optical waveguide.
 6. A planar lightwavecircuit as defined in claim 2, wherein at least one of said modecoupling means and said mode re-coupling means includes at least oneinsular core portion which is spaced from the core of said opticalwaveguide.
 7. A planar lightwave circuit as defined in any of claims 1,wherein at least one of said mode coupling means and said modere-coupling means includes at least one insular clad portion having arefractive index equal to that of the clad, within the core of theoptical waveguide.
 8. A planar lightwave circuit as defined in any ofclaims 2, wherein at least one of said mode coupling means and said modere-coupling means includes at least one insular clad portion having arefractive index equal to that of the clad, within the core of theoptical waveguide.
 9. A planar lightwave circuit comprising an opticalwaveguide lens which has a core and a clad formed on a substrate,wherein the optical waveguide lens comprises: at least one input opticalwaveguide which inputs signal light; mode coupling means for couplingpart of the inputted signal light to a higher-order mode and a radiationmode; mode re-coupling means for re-coupling the signal light coupled tothe higher-order mode and the radiation mode by said mode couplingmeans, to output signal light; and at least one output optical waveguidefor outputting the output signal light; said mode coupling means andsaid mode re-coupling means being optical waveguides each of which hasat least one of a core width and height varied irregularly continuously.10. A planar lightwave circuit comprising a cross waveguide in which atleast two optical waveguides having a core and a clad formed on asubstrate cross, wherein the cross waveguide comprises: at least twoinput optical waveguides which input signal light; mode coupling meansfor coupling part of the inputted signal light to a higher-order modeand a radiation mode; mode re-coupling means for re-coupling the signallight coupled to the higher-order mode and the radiation mode by saidmode coupling means, to output signal light; at least two output opticalwaveguides which output the output signal light, and anoptical-waveguide crossing portion being a part at which two virtualoptical waveguides rectilinearly extending from the input waveguidestoward the output waveguides overlap; said mode coupling means and saidmode re-coupling means being optical waveguides each of which has a corewidth varied continuously; said optical-waveguide crossing portion beingsuch that a core width of an optical waveguide at a position between anend of said optical-waveguide crossing portion on a side of said inputoptical waveguides and a central part of said optical-waveguide crossingportion is greater than the core width of the optical waveguide at anend of said optical-waveguide crossing portion on the side of said inputoptical waveguides and the core width of the optical waveguide at thecentral part of said optical-waveguide crossing portion, and that thecore width of the optical waveguide at a position between the centralpart of said optical-waveguide crossing portion and an end of saidoptical-waveguide crossing portion on a side of said output opticalwaveguides is greater than the core width of the optical waveguide atthe central part of said optical-waveguide crossing portion and the corewidth of the optical waveguide at the end of said optical-waveguidecrossing portion on the side of said output optical waveguides.
 11. Aplanar lightwave circuit comprising an optical branch circuit which hasa core and a clad formed on a substrate, wherein the optical branchcircuit comprises: one input optical waveguide which inputs signallight; mode coupling means for coupling part of the inputted signallight to a higher-order mode and a radiation mode; mode re-couplingmeans for re-coupling the signal light coupled to the higher-order modeand the radiation mode by said mode coupling means, to output signallight; and at least two output optical waveguides which output theoutput signal light; said mode coupling means and said mode re-couplingmeans being optical waveguides each of which has a core width variedirregularly continuously.
 12. A planar lightwave circuit comprising aslab type coupler which has a core and a clad formed on a substrate,wherein the slab type coupler comprises: at least one, firstinput/output optical waveguide which inputs/outputs a light signal; anoptical slab waveguide which is optically connected to the first inputoptical waveguide; and at least two, second input/output opticalwaveguides which are optically connected to said optical slab waveguide,and which input/output light signals; and that said second input/outputoptical waveguides comprise mode coupling means for coupling part of theinputted/outputted signal light to at least either of a higher-ordermode and a radiation mode, and converting the coupled part into a planewave at an end of said optical slab waveguide; said mode coupling meansbeing an optical waveguide which has a core width varied irregularlycontinuously.
 13. A planar lightwave circuit comprising an arrayedwaveguide grating filter which has a core and a clad formed on asubstrate, wherein the arrayed waveguide grating filter comprises: atleast one input optical waveguide which inputs signal light; a firstoptical slab waveguide which is optically connected with said inputoptical waveguide; arrayed optical waveguides which are opticallyconnected with said first optical slab waveguide, and which becomelonger with a predetermined waveguide length difference in succession; asecond optical slab waveguide which is optically connected to saidarrayed optical waveguides; and at least one output optical waveguidewhich is optically connected to said second optical slab waveguide; andthat each of said arrayed optical waveguides comprises: mode re-couplingmeans for re-coupling a higher-order mode and a radiation mode to thesignal light, at a part optically touching said first optical slabwaveguide; and mode coupling means for coupling the signal light to thehigher-order mode and the radiation mode, at a part optically touchingsaid second optical slab waveguide; said mode coupling means and saidmode re-coupling means being optical waveguides each of which has a corewidth varied irregularly continuously.